Matemática básica Exemplos

$(\frac{\sqrt{b}}{a - \sqrt{a b}} - \frac{\sqrt{a}}{\sqrt{a b} - b}) (a \sqrt{b} - b \sqrt{a})$

Etapa 1

Simplifique cada termo.

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Etapa 1.1

Simplifique o denominador.

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Etapa 1.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ para reescrever $\sqrt{a b}$ como ${(a b)}^{\frac{1}{2}}$ .

$(\frac{\sqrt{b}}{a - {(a b)}^{\frac{1}{2}}} - \frac{\sqrt{a}}{\sqrt{a b} - b}) (a \sqrt{b} - b \sqrt{a})$

Etapa 1.1.2

Aplique a regra do produto a $a b$ .

$(\frac{\sqrt{b}}{a - (a^{\frac{1}{2}} b^{\frac{1}{2}})} - \frac{\sqrt{a}}{\sqrt{a b} - b}) (a \sqrt{b} - b \sqrt{a})$

Etapa 1.1.3

Reescreva $a - a^{\frac{1}{2}} b^{\frac{1}{2}}$ em uma forma fatorada.

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Etapa 1.1.3.1

Fatore $a^{\frac{1}{2}}$ de $a - a^{\frac{1}{2}} b^{\frac{1}{2}}$ .

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Etapa 1.1.3.1.1

Eleve $a$ à potência de $1$ .

$(\frac{\sqrt{b}}{a^{1} - a^{\frac{1}{2}} b^{\frac{1}{2}}} - \frac{\sqrt{a}}{\sqrt{a b} - b}) (a \sqrt{b} - b \sqrt{a})$

Etapa 1.1.3.1.2

Fatore $a^{\frac{1}{2}}$ de $a^{1}$ .

$(\frac{\sqrt{b}}{a^{\frac{1}{2}} a^{\frac{1}{2}} - a^{\frac{1}{2}} b^{\frac{1}{2}}} - \frac{\sqrt{a}}{\sqrt{a b} - b}) (a \sqrt{b} - b \sqrt{a})$

Etapa 1.1.3.1.3

Fatore $a^{\frac{1}{2}}$ de $- a^{\frac{1}{2}} b^{\frac{1}{2}}$ .

$(\frac{\sqrt{b}}{a^{\frac{1}{2}} a^{\frac{1}{2}} + a^{\frac{1}{2}} (- 1 b^{\frac{1}{2}})} - \frac{\sqrt{a}}{\sqrt{a b} - b}) (a \sqrt{b} - b \sqrt{a})$

Etapa 1.1.3.1.4

Fatore $a^{\frac{1}{2}}$ de $a^{\frac{1}{2}} a^{\frac{1}{2}} + a^{\frac{1}{2}} (- 1 b^{\frac{1}{2}})$ .

$(\frac{\sqrt{b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - 1 b^{\frac{1}{2}})} - \frac{\sqrt{a}}{\sqrt{a b} - b}) (a \sqrt{b} - b \sqrt{a})$

Etapa 1.1.3.2

Reescreva $- 1 b^{\frac{1}{2}}$ como $- b^{\frac{1}{2}}$ .

$(\frac{\sqrt{b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} - \frac{\sqrt{a}}{\sqrt{a b} - b}) (a \sqrt{b} - b \sqrt{a})$

Etapa 1.2

Simplifique o denominador.

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Etapa 1.2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ para reescrever $\sqrt{a b}$ como ${(a b)}^{\frac{1}{2}}$ .

$(\frac{\sqrt{b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} - \frac{\sqrt{a}}{{(a b)}^{\frac{1}{2}} - b}) (a \sqrt{b} - b \sqrt{a})$

Etapa 1.2.2

Aplique a regra do produto a $a b$ .

$(\frac{\sqrt{b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} - \frac{\sqrt{a}}{a^{\frac{1}{2}} b^{\frac{1}{2}} - b}) (a \sqrt{b} - b \sqrt{a})$

Etapa 1.2.3

Fatore $b^{\frac{1}{2}}$ de $a^{\frac{1}{2}} b^{\frac{1}{2}} - b$ .

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Etapa 1.2.3.1

Fatore $b^{\frac{1}{2}}$ de $a^{\frac{1}{2}} b^{\frac{1}{2}}$ .

$(\frac{\sqrt{b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} - \frac{\sqrt{a}}{b^{\frac{1}{2}} a^{\frac{1}{2}} - b}) (a \sqrt{b} - b \sqrt{a})$

Etapa 1.2.3.2

Fatore $b^{\frac{1}{2}}$ de $- b$ .

$(\frac{\sqrt{b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} - \frac{\sqrt{a}}{b^{\frac{1}{2}} a^{\frac{1}{2}} + b^{\frac{1}{2}} (- b^{\frac{1}{2}})}) (a \sqrt{b} - b \sqrt{a})$

Etapa 1.2.3.3

Fatore $b^{\frac{1}{2}}$ de $b^{\frac{1}{2}} a^{\frac{1}{2}} + b^{\frac{1}{2}} (- b^{\frac{1}{2}})$ .

$(\frac{\sqrt{b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}) (a \sqrt{b} - b \sqrt{a})$

Etapa 2

Expanda $(\frac{\sqrt{b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}) (a \sqrt{b} - b \sqrt{a})$ usando o método FOIL.

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Etapa 2.1

Aplique a propriedade distributiva.

$\frac{\sqrt{b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (a \sqrt{b} - b \sqrt{a}) - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (a \sqrt{b} - b \sqrt{a})$

Etapa 2.2

Aplique a propriedade distributiva.

$\frac{\sqrt{b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (a \sqrt{b}) + \frac{\sqrt{b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (- b \sqrt{a}) - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (a \sqrt{b} - b \sqrt{a})$

Etapa 2.3

Aplique a propriedade distributiva.

Etapa 3

Simplifique e combine termos semelhantes.

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Etapa 3.1

Simplifique cada termo.

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Etapa 3.1.1

Multiplique $\frac{\sqrt{b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (a \sqrt{b})$ .

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Etapa 3.1.1.1

Combine $a$ e $\frac{\sqrt{b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$ .

$\frac{a \sqrt{b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} \sqrt{b} + \frac{\sqrt{b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (- b \sqrt{a}) - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (a \sqrt{b}) - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (- b \sqrt{a})$

Etapa 3.1.1.2

Combine $\frac{a \sqrt{b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$ e $\sqrt{b}$ .

$\frac{a \sqrt{b} \sqrt{b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} + \frac{\sqrt{b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (- b \sqrt{a}) - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (a \sqrt{b}) - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (- b \sqrt{a})$

Etapa 3.1.1.3

Eleve $\sqrt{b}$ à potência de $1$ .

$\frac{a ({\sqrt{b}}^{1} \sqrt{b})}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} + \frac{\sqrt{b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (- b \sqrt{a}) - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (a \sqrt{b}) - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (- b \sqrt{a})$

Etapa 3.1.1.4

Eleve $\sqrt{b}$ à potência de $1$ .

$\frac{a ({\sqrt{b}}^{1} {\sqrt{b}}^{1})}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} + \frac{\sqrt{b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (- b \sqrt{a}) - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (a \sqrt{b}) - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (- b \sqrt{a})$

Etapa 3.1.1.5

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$\frac{a {\sqrt{b}}^{1 + 1}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} + \frac{\sqrt{b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (- b \sqrt{a}) - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (a \sqrt{b}) - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (- b \sqrt{a})$

Etapa 3.1.1.6

Some $1$ e $1$ .

$\frac{a {\sqrt{b}}^{2}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} + \frac{\sqrt{b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (- b \sqrt{a}) - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (a \sqrt{b}) - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (- b \sqrt{a})$

Etapa 3.1.2

Mova $a^{\frac{1}{2}}$ para o numerador usando a regra do expoente negativo $\frac{1}{b^{n}} = b^{- n}$ .

$\frac{a {\sqrt{b}}^{2} a^{- \frac{1}{2}}}{a^{\frac{1}{2}} - b^{\frac{1}{2}}} + \frac{\sqrt{b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (- b \sqrt{a}) - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (a \sqrt{b}) - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (- b \sqrt{a})$

Etapa 3.1.3

Multiplique $a$ por $a^{- \frac{1}{2}}$ somando os expoentes.

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Etapa 3.1.3.1

Mova $a^{- \frac{1}{2}}$ .

$\frac{a^{- \frac{1}{2}} a {\sqrt{b}}^{2}}{a^{\frac{1}{2}} - b^{\frac{1}{2}}} + \frac{\sqrt{b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (- b \sqrt{a}) - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (a \sqrt{b}) - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (- b \sqrt{a})$

Etapa 3.1.3.2

Multiplique $a^{- \frac{1}{2}}$ por $a$ .

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Etapa 3.1.3.2.1

Eleve $a$ à potência de $1$ .

$\frac{a^{- \frac{1}{2}} a^{1} {\sqrt{b}}^{2}}{a^{\frac{1}{2}} - b^{\frac{1}{2}}} + \frac{\sqrt{b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (- b \sqrt{a}) - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (a \sqrt{b}) - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (- b \sqrt{a})$

Etapa 3.1.3.2.2

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$\frac{a^{- \frac{1}{2} + 1} {\sqrt{b}}^{2}}{a^{\frac{1}{2}} - b^{\frac{1}{2}}} + \frac{\sqrt{b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (- b \sqrt{a}) - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (a \sqrt{b}) - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (- b \sqrt{a})$

Etapa 3.1.3.3

Escreva $1$ como uma fração com um denominador comum.

$\frac{a^{- \frac{1}{2} + \frac{2}{2}} {\sqrt{b}}^{2}}{a^{\frac{1}{2}} - b^{\frac{1}{2}}} + \frac{\sqrt{b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (- b \sqrt{a}) - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (a \sqrt{b}) - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (- b \sqrt{a})$

Etapa 3.1.3.4

Combine os numeradores em relação ao denominador comum.

$\frac{a^{\frac{- 1 + 2}{2}} {\sqrt{b}}^{2}}{a^{\frac{1}{2}} - b^{\frac{1}{2}}} + \frac{\sqrt{b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (- b \sqrt{a}) - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (a \sqrt{b}) - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (- b \sqrt{a})$

Etapa 3.1.3.5

Some $- 1$ e $2$ .

$\frac{a^{\frac{1}{2}} {\sqrt{b}}^{2}}{a^{\frac{1}{2}} - b^{\frac{1}{2}}} + \frac{\sqrt{b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (- b \sqrt{a}) - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (a \sqrt{b}) - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (- b \sqrt{a})$

Etapa 3.1.4

Reescreva ${\sqrt{b}}^{2}$ como $b$ .

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Etapa 3.1.4.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ para reescrever $\sqrt{b}$ como $b^{\frac{1}{2}}$ .

$\frac{a^{\frac{1}{2}} {(b^{\frac{1}{2}})}^{2}}{a^{\frac{1}{2}} - b^{\frac{1}{2}}} + \frac{\sqrt{b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (- b \sqrt{a}) - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (a \sqrt{b}) - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (- b \sqrt{a})$

Etapa 3.1.4.2

Aplique a regra da multiplicação de potências e multiplique os expoentes, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{a^{\frac{1}{2}} b^{\frac{1}{2} \cdot 2}}{a^{\frac{1}{2}} - b^{\frac{1}{2}}} + \frac{\sqrt{b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (- b \sqrt{a}) - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (a \sqrt{b}) - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (- b \sqrt{a})$

Etapa 3.1.4.3

Combine $\frac{1}{2}$ e $2$ .

$\frac{a^{\frac{1}{2}} b^{\frac{2}{2}}}{a^{\frac{1}{2}} - b^{\frac{1}{2}}} + \frac{\sqrt{b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (- b \sqrt{a}) - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (a \sqrt{b}) - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (- b \sqrt{a})$

Etapa 3.1.4.4

Cancele o fator comum de $2$ .

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Etapa 3.1.4.4.1

Cancele o fator comum.

Etapa 3.1.4.4.2

Reescreva a expressão.

$\frac{a^{\frac{1}{2}} b^{1}}{a^{\frac{1}{2}} - b^{\frac{1}{2}}} + \frac{\sqrt{b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (- b \sqrt{a}) - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (a \sqrt{b}) - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (- b \sqrt{a})$

Etapa 3.1.4.5

Simplifique.

$\frac{a^{\frac{1}{2}} b}{a^{\frac{1}{2}} - b^{\frac{1}{2}}} + \frac{\sqrt{b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (- b \sqrt{a}) - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (a \sqrt{b}) - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (- b \sqrt{a})$

Etapa 3.1.5

Reescreva usando a propriedade comutativa da multiplicação.

$\frac{a^{\frac{1}{2}} b}{a^{\frac{1}{2}} - b^{\frac{1}{2}}} - \frac{\sqrt{b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (b \sqrt{a}) - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (a \sqrt{b}) - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (- b \sqrt{a})$

Etapa 3.1.6

Multiplique $- \frac{\sqrt{b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (b \sqrt{a})$ .

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Etapa 3.1.6.1

Combine $b$ e $\frac{\sqrt{b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$ .

$\frac{a^{\frac{1}{2}} b}{a^{\frac{1}{2}} - b^{\frac{1}{2}}} - \frac{b \sqrt{b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} \sqrt{a} - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (a \sqrt{b}) - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (- b \sqrt{a})$

Etapa 3.1.6.2

Combine $\sqrt{a}$ e $\frac{b \sqrt{b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$ .

$\frac{a^{\frac{1}{2}} b}{a^{\frac{1}{2}} - b^{\frac{1}{2}}} - \frac{\sqrt{a} (b \sqrt{b})}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (a \sqrt{b}) - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (- b \sqrt{a})$

Etapa 3.1.6.3

Combine usando a regra do produto para radicais.

$\frac{a^{\frac{1}{2}} b}{a^{\frac{1}{2}} - b^{\frac{1}{2}}} - \frac{b \sqrt{a b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (a \sqrt{b}) - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (- b \sqrt{a})$

Etapa 3.1.7

Multiplique $- \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (a \sqrt{b})$ .

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Etapa 3.1.7.1

Combine $a$ e $\frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$ .

$\frac{a^{\frac{1}{2}} b}{a^{\frac{1}{2}} - b^{\frac{1}{2}}} - \frac{b \sqrt{a b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} - \frac{a \sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} \sqrt{b} - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (- b \sqrt{a})$

Etapa 3.1.7.2

Combine $\sqrt{b}$ e $\frac{a \sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$ .

$\frac{a^{\frac{1}{2}} b}{a^{\frac{1}{2}} - b^{\frac{1}{2}}} - \frac{b \sqrt{a b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} - \frac{\sqrt{b} (a \sqrt{a})}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (- b \sqrt{a})$

Etapa 3.1.7.3

Combine usando a regra do produto para radicais.

$\frac{a^{\frac{1}{2}} b}{a^{\frac{1}{2}} - b^{\frac{1}{2}}} - \frac{b \sqrt{a b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} - \frac{a \sqrt{b a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} - \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (- b \sqrt{a})$

Etapa 3.1.8

Multiplique $- \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (- b \sqrt{a})$ .

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Etapa 3.1.8.1

Multiplique $- 1$ por $- 1$ .

$\frac{a^{\frac{1}{2}} b}{a^{\frac{1}{2}} - b^{\frac{1}{2}}} - \frac{b \sqrt{a b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} - \frac{a \sqrt{b a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} + 1 \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (b \sqrt{a})$

Etapa 3.1.8.2

Multiplique $\frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$ por $1$ .

$\frac{a^{\frac{1}{2}} b}{a^{\frac{1}{2}} - b^{\frac{1}{2}}} - \frac{b \sqrt{a b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} - \frac{a \sqrt{b a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} + \frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} (b \sqrt{a})$

Etapa 3.1.8.3

Combine $b$ e $\frac{\sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$ .

$\frac{a^{\frac{1}{2}} b}{a^{\frac{1}{2}} - b^{\frac{1}{2}}} - \frac{b \sqrt{a b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} - \frac{a \sqrt{b a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} + \frac{b \sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} \sqrt{a}$

Etapa 3.1.8.4

Combine $\frac{b \sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$ e $\sqrt{a}$ .

$\frac{a^{\frac{1}{2}} b}{a^{\frac{1}{2}} - b^{\frac{1}{2}}} - \frac{b \sqrt{a b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} - \frac{a \sqrt{b a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} + \frac{b \sqrt{a} \sqrt{a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 3.1.8.5

Eleve $\sqrt{a}$ à potência de $1$ .

$\frac{a^{\frac{1}{2}} b}{a^{\frac{1}{2}} - b^{\frac{1}{2}}} - \frac{b \sqrt{a b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} - \frac{a \sqrt{b a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} + \frac{b ({\sqrt{a}}^{1} \sqrt{a})}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 3.1.8.6

Eleve $\sqrt{a}$ à potência de $1$ .

$\frac{a^{\frac{1}{2}} b}{a^{\frac{1}{2}} - b^{\frac{1}{2}}} - \frac{b \sqrt{a b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} - \frac{a \sqrt{b a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} + \frac{b ({\sqrt{a}}^{1} {\sqrt{a}}^{1})}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 3.1.8.7

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$\frac{a^{\frac{1}{2}} b}{a^{\frac{1}{2}} - b^{\frac{1}{2}}} - \frac{b \sqrt{a b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} - \frac{a \sqrt{b a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} + \frac{b {\sqrt{a}}^{1 + 1}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 3.1.8.8

Some $1$ e $1$ .

$\frac{a^{\frac{1}{2}} b}{a^{\frac{1}{2}} - b^{\frac{1}{2}}} - \frac{b \sqrt{a b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} - \frac{a \sqrt{b a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} + \frac{b {\sqrt{a}}^{2}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 3.1.9

Mova $b^{\frac{1}{2}}$ para o numerador usando a regra do expoente negativo $\frac{1}{b^{n}} = b^{- n}$ .

$\frac{a^{\frac{1}{2}} b}{a^{\frac{1}{2}} - b^{\frac{1}{2}}} - \frac{b \sqrt{a b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} - \frac{a \sqrt{b a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} + \frac{b {\sqrt{a}}^{2} b^{- \frac{1}{2}}}{a^{\frac{1}{2}} - b^{\frac{1}{2}}}$

Etapa 3.1.10

Multiplique $b$ por $b^{- \frac{1}{2}}$ somando os expoentes.

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Etapa 3.1.10.1

Mova $b^{- \frac{1}{2}}$ .

$\frac{a^{\frac{1}{2}} b}{a^{\frac{1}{2}} - b^{\frac{1}{2}}} - \frac{b \sqrt{a b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} - \frac{a \sqrt{b a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} + \frac{b^{- \frac{1}{2}} b {\sqrt{a}}^{2}}{a^{\frac{1}{2}} - b^{\frac{1}{2}}}$

Etapa 3.1.10.2

Multiplique $b^{- \frac{1}{2}}$ por $b$ .

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Etapa 3.1.10.2.1

Eleve $b$ à potência de $1$ .

$\frac{a^{\frac{1}{2}} b}{a^{\frac{1}{2}} - b^{\frac{1}{2}}} - \frac{b \sqrt{a b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} - \frac{a \sqrt{b a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} + \frac{b^{- \frac{1}{2}} b^{1} {\sqrt{a}}^{2}}{a^{\frac{1}{2}} - b^{\frac{1}{2}}}$

Etapa 3.1.10.2.2

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$\frac{a^{\frac{1}{2}} b}{a^{\frac{1}{2}} - b^{\frac{1}{2}}} - \frac{b \sqrt{a b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} - \frac{a \sqrt{b a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} + \frac{b^{- \frac{1}{2} + 1} {\sqrt{a}}^{2}}{a^{\frac{1}{2}} - b^{\frac{1}{2}}}$

Etapa 3.1.10.3

Escreva $1$ como uma fração com um denominador comum.

$\frac{a^{\frac{1}{2}} b}{a^{\frac{1}{2}} - b^{\frac{1}{2}}} - \frac{b \sqrt{a b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} - \frac{a \sqrt{b a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} + \frac{b^{- \frac{1}{2} + \frac{2}{2}} {\sqrt{a}}^{2}}{a^{\frac{1}{2}} - b^{\frac{1}{2}}}$

Etapa 3.1.10.4

Combine os numeradores em relação ao denominador comum.

$\frac{a^{\frac{1}{2}} b}{a^{\frac{1}{2}} - b^{\frac{1}{2}}} - \frac{b \sqrt{a b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} - \frac{a \sqrt{b a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} + \frac{b^{\frac{- 1 + 2}{2}} {\sqrt{a}}^{2}}{a^{\frac{1}{2}} - b^{\frac{1}{2}}}$

Etapa 3.1.10.5

Some $- 1$ e $2$ .

$\frac{a^{\frac{1}{2}} b}{a^{\frac{1}{2}} - b^{\frac{1}{2}}} - \frac{b \sqrt{a b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} - \frac{a \sqrt{b a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} + \frac{b^{\frac{1}{2}} {\sqrt{a}}^{2}}{a^{\frac{1}{2}} - b^{\frac{1}{2}}}$

Etapa 3.1.11

Reescreva ${\sqrt{a}}^{2}$ como $a$ .

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Etapa 3.1.11.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ para reescrever $\sqrt{a}$ como $a^{\frac{1}{2}}$ .

$\frac{a^{\frac{1}{2}} b}{a^{\frac{1}{2}} - b^{\frac{1}{2}}} - \frac{b \sqrt{a b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} - \frac{a \sqrt{b a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} + \frac{b^{\frac{1}{2}} {(a^{\frac{1}{2}})}^{2}}{a^{\frac{1}{2}} - b^{\frac{1}{2}}}$

Etapa 3.1.11.2

Aplique a regra da multiplicação de potências e multiplique os expoentes, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{a^{\frac{1}{2}} b}{a^{\frac{1}{2}} - b^{\frac{1}{2}}} - \frac{b \sqrt{a b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} - \frac{a \sqrt{b a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} + \frac{b^{\frac{1}{2}} a^{\frac{1}{2} \cdot 2}}{a^{\frac{1}{2}} - b^{\frac{1}{2}}}$

Etapa 3.1.11.3

Combine $\frac{1}{2}$ e $2$ .

$\frac{a^{\frac{1}{2}} b}{a^{\frac{1}{2}} - b^{\frac{1}{2}}} - \frac{b \sqrt{a b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} - \frac{a \sqrt{b a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} + \frac{b^{\frac{1}{2}} a^{\frac{2}{2}}}{a^{\frac{1}{2}} - b^{\frac{1}{2}}}$

Etapa 3.1.11.4

Cancele o fator comum de $2$ .

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Etapa 3.1.11.4.1

Cancele o fator comum.

$\frac{a^{\frac{1}{2}} b}{a^{\frac{1}{2}} - b^{\frac{1}{2}}} - \frac{b \sqrt{a b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} - \frac{a \sqrt{b a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} + \frac{b^{\frac{1}{2}} a^{\frac{2}{2}}}{a^{\frac{1}{2}} - b^{\frac{1}{2}}}$

Etapa 3.1.11.4.2

Reescreva a expressão.

$\frac{a^{\frac{1}{2}} b}{a^{\frac{1}{2}} - b^{\frac{1}{2}}} - \frac{b \sqrt{a b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} - \frac{a \sqrt{b a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} + \frac{b^{\frac{1}{2}} a^{1}}{a^{\frac{1}{2}} - b^{\frac{1}{2}}}$

Etapa 3.1.11.5

Simplifique.

$\frac{a^{\frac{1}{2}} b}{a^{\frac{1}{2}} - b^{\frac{1}{2}}} - \frac{b \sqrt{a b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} - \frac{a \sqrt{b a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} + \frac{b^{\frac{1}{2}} a}{a^{\frac{1}{2}} - b^{\frac{1}{2}}}$

Etapa 3.2

Para escrever $\frac{a^{\frac{1}{2}} b}{a^{\frac{1}{2}} - b^{\frac{1}{2}}}$ como fração com um denominador comum, multiplique por $\frac{a^{\frac{1}{2}}}{a^{\frac{1}{2}}}$ .

$\frac{a^{\frac{1}{2}} b}{a^{\frac{1}{2}} - b^{\frac{1}{2}}} \cdot \frac{a^{\frac{1}{2}}}{a^{\frac{1}{2}}} - \frac{b \sqrt{a b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} - \frac{a \sqrt{b a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} + \frac{b^{\frac{1}{2}} a}{a^{\frac{1}{2}} - b^{\frac{1}{2}}}$

Etapa 3.3

Escreva cada expressão com um denominador comum de $(a^{\frac{1}{2}} - b^{\frac{1}{2}}) a^{\frac{1}{2}}$ , multiplicando cada um por um fator apropriado de $1$ .

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Etapa 3.3.1

Multiplique $\frac{a^{\frac{1}{2}} b}{a^{\frac{1}{2}} - b^{\frac{1}{2}}}$ por $\frac{a^{\frac{1}{2}}}{a^{\frac{1}{2}}}$ .

$\frac{a^{\frac{1}{2}} b a^{\frac{1}{2}}}{(a^{\frac{1}{2}} - b^{\frac{1}{2}}) a^{\frac{1}{2}}} - \frac{b \sqrt{a b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} - \frac{a \sqrt{b a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} + \frac{b^{\frac{1}{2}} a}{a^{\frac{1}{2}} - b^{\frac{1}{2}}}$

Etapa 3.3.2

Reordene os fatores de $(a^{\frac{1}{2}} - b^{\frac{1}{2}}) a^{\frac{1}{2}}$ .

$\frac{a^{\frac{1}{2}} b a^{\frac{1}{2}}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} - \frac{b \sqrt{a b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} - \frac{a \sqrt{b a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} + \frac{b^{\frac{1}{2}} a}{a^{\frac{1}{2}} - b^{\frac{1}{2}}}$

Etapa 3.4

Combine os numeradores em relação ao denominador comum.

$\frac{a^{\frac{1}{2}} b a^{\frac{1}{2}} - b \sqrt{a b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} - \frac{a \sqrt{b a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} + \frac{b^{\frac{1}{2}} a}{a^{\frac{1}{2}} - b^{\frac{1}{2}}}$

Etapa 3.5

Para escrever $\frac{a^{\frac{1}{2}} b a^{\frac{1}{2}} - b \sqrt{a b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$ como fração com um denominador comum, multiplique por $\frac{b^{\frac{1}{2}}}{b^{\frac{1}{2}}}$ .

$\frac{a^{\frac{1}{2}} b a^{\frac{1}{2}} - b \sqrt{a b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} \cdot \frac{b^{\frac{1}{2}}}{b^{\frac{1}{2}}} - \frac{a \sqrt{b a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} + \frac{b^{\frac{1}{2}} a}{a^{\frac{1}{2}} - b^{\frac{1}{2}}}$

Etapa 3.6

Para escrever $- \frac{a \sqrt{b a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$ como fração com um denominador comum, multiplique por $\frac{a^{\frac{1}{2}}}{a^{\frac{1}{2}}}$ .

$\frac{a^{\frac{1}{2}} b a^{\frac{1}{2}} - b \sqrt{a b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} \cdot \frac{b^{\frac{1}{2}}}{b^{\frac{1}{2}}} - \frac{a \sqrt{b a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} \cdot \frac{a^{\frac{1}{2}}}{a^{\frac{1}{2}}} + \frac{b^{\frac{1}{2}} a}{a^{\frac{1}{2}} - b^{\frac{1}{2}}}$

Etapa 3.7

Escreva cada expressão com um denominador comum de $(a^{\frac{1}{2}} - b^{\frac{1}{2}}) a^{\frac{1}{2}} b^{\frac{1}{2}}$ , multiplicando cada um por um fator apropriado de $1$ .

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Etapa 3.7.1

Multiplique $\frac{a^{\frac{1}{2}} b a^{\frac{1}{2}} - b \sqrt{a b}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$ por $\frac{b^{\frac{1}{2}}}{b^{\frac{1}{2}}}$ .

$\frac{(a^{\frac{1}{2}} b a^{\frac{1}{2}} - b \sqrt{a b}) b^{\frac{1}{2}}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}}) b^{\frac{1}{2}}} - \frac{a \sqrt{b a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} \cdot \frac{a^{\frac{1}{2}}}{a^{\frac{1}{2}}} + \frac{b^{\frac{1}{2}} a}{a^{\frac{1}{2}} - b^{\frac{1}{2}}}$

Etapa 3.7.2

Multiplique $\frac{a \sqrt{b a}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$ por $\frac{a^{\frac{1}{2}}}{a^{\frac{1}{2}}}$ .

$\frac{(a^{\frac{1}{2}} b a^{\frac{1}{2}} - b \sqrt{a b}) b^{\frac{1}{2}}}{a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}}) b^{\frac{1}{2}}} - \frac{a \sqrt{b a} a^{\frac{1}{2}}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}}) a^{\frac{1}{2}}} + \frac{b^{\frac{1}{2}} a}{a^{\frac{1}{2}} - b^{\frac{1}{2}}}$

Etapa 3.7.3

Reordene os fatores de $a^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}}) b^{\frac{1}{2}}$ .

$\frac{(a^{\frac{1}{2}} b a^{\frac{1}{2}} - b \sqrt{a b}) b^{\frac{1}{2}}}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} - \frac{a \sqrt{b a} a^{\frac{1}{2}}}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}}) a^{\frac{1}{2}}} + \frac{b^{\frac{1}{2}} a}{a^{\frac{1}{2}} - b^{\frac{1}{2}}}$

Etapa 3.7.4

Reordene os fatores de $b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}}) a^{\frac{1}{2}}$ .

$\frac{(a^{\frac{1}{2}} b a^{\frac{1}{2}} - b \sqrt{a b}) b^{\frac{1}{2}}}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} - \frac{a \sqrt{b a} a^{\frac{1}{2}}}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} + \frac{b^{\frac{1}{2}} a}{a^{\frac{1}{2}} - b^{\frac{1}{2}}}$

Etapa 3.8

Combine os numeradores em relação ao denominador comum.

$\frac{(a^{\frac{1}{2}} b a^{\frac{1}{2}} - b \sqrt{a b}) b^{\frac{1}{2}} - a \sqrt{b a} a^{\frac{1}{2}}}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})} + \frac{b^{\frac{1}{2}} a}{a^{\frac{1}{2}} - b^{\frac{1}{2}}}$

Etapa 3.9

Para escrever $\frac{b^{\frac{1}{2}} a}{a^{\frac{1}{2}} - b^{\frac{1}{2}}}$ como fração com um denominador comum, multiplique por $\frac{a^{\frac{1}{2}} b^{\frac{1}{2}}}{a^{\frac{1}{2}} b^{\frac{1}{2}}}$ .

Etapa 3.10

Escreva cada expressão com um denominador comum de $(a^{\frac{1}{2}} - b^{\frac{1}{2}}) a^{\frac{1}{2}} b^{\frac{1}{2}}$ , multiplicando cada um por um fator apropriado de $1$ .

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Etapa 3.10.1

Multiplique $\frac{b^{\frac{1}{2}} a}{a^{\frac{1}{2}} - b^{\frac{1}{2}}}$ por $\frac{a^{\frac{1}{2}} b^{\frac{1}{2}}}{a^{\frac{1}{2}} b^{\frac{1}{2}}}$ .

Etapa 3.10.2

Reordene os fatores de $(a^{\frac{1}{2}} - b^{\frac{1}{2}}) (a^{\frac{1}{2}} b^{\frac{1}{2}})$ .

Etapa 3.11

Combine os numeradores em relação ao denominador comum.

$\frac{(a^{\frac{1}{2}} b a^{\frac{1}{2}} - b \sqrt{a b}) b^{\frac{1}{2}} - a \sqrt{b a} a^{\frac{1}{2}} + b^{\frac{1}{2}} a (a^{\frac{1}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4

Simplifique o numerador.

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Etapa 4.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ para reescrever $\sqrt{a b}$ como ${(a b)}^{\frac{1}{2}}$ .

$\frac{(a^{\frac{1}{2}} b a^{\frac{1}{2}} - b {(a b)}^{\frac{1}{2}}) b^{\frac{1}{2}} - a \sqrt{b a} a^{\frac{1}{2}} + b^{\frac{1}{2}} a (a^{\frac{1}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ para reescrever $\sqrt{b a}$ como ${(b a)}^{\frac{1}{2}}$ .

$\frac{(a^{\frac{1}{2}} b a^{\frac{1}{2}} - b {(a b)}^{\frac{1}{2}}) b^{\frac{1}{2}} - a {(b a)}^{\frac{1}{2}} a^{\frac{1}{2}} + b^{\frac{1}{2}} a (a^{\frac{1}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.3

Simplifique cada termo.

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Etapa 4.3.1

Multiplique $a^{\frac{1}{2}}$ por $a^{\frac{1}{2}}$ somando os expoentes.

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Etapa 4.3.1.1

Mova $a^{\frac{1}{2}}$ .

$\frac{(a^{\frac{1}{2}} a^{\frac{1}{2}} b - b {(a b)}^{\frac{1}{2}}) b^{\frac{1}{2}} - a {(b a)}^{\frac{1}{2}} a^{\frac{1}{2}} + b^{\frac{1}{2}} a (a^{\frac{1}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.3.1.2

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$\frac{(a^{\frac{1}{2} + \frac{1}{2}} b - b {(a b)}^{\frac{1}{2}}) b^{\frac{1}{2}} - a {(b a)}^{\frac{1}{2}} a^{\frac{1}{2}} + b^{\frac{1}{2}} a (a^{\frac{1}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.3.1.3

Combine os numeradores em relação ao denominador comum.

$\frac{(a^{\frac{1 + 1}{2}} b - b {(a b)}^{\frac{1}{2}}) b^{\frac{1}{2}} - a {(b a)}^{\frac{1}{2}} a^{\frac{1}{2}} + b^{\frac{1}{2}} a (a^{\frac{1}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.3.1.4

Some $1$ e $1$ .

$\frac{(a^{\frac{2}{2}} b - b {(a b)}^{\frac{1}{2}}) b^{\frac{1}{2}} - a {(b a)}^{\frac{1}{2}} a^{\frac{1}{2}} + b^{\frac{1}{2}} a (a^{\frac{1}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.3.1.5

Divida $2$ por $2$ .

$\frac{(a^{1} b - b {(a b)}^{\frac{1}{2}}) b^{\frac{1}{2}} - a {(b a)}^{\frac{1}{2}} a^{\frac{1}{2}} + b^{\frac{1}{2}} a (a^{\frac{1}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.3.2

Simplifique $a^{1} b$ .

$\frac{(a b - b {(a b)}^{\frac{1}{2}}) b^{\frac{1}{2}} - a {(b a)}^{\frac{1}{2}} a^{\frac{1}{2}} + b^{\frac{1}{2}} a (a^{\frac{1}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.3.3

Aplique a regra do produto a $a b$ .

$\frac{(a b - b (a^{\frac{1}{2}} b^{\frac{1}{2}})) b^{\frac{1}{2}} - a {(b a)}^{\frac{1}{2}} a^{\frac{1}{2}} + b^{\frac{1}{2}} a (a^{\frac{1}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.3.4

Multiplique $b$ por $b^{\frac{1}{2}}$ somando os expoentes.

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Etapa 4.3.4.1

Mova $b^{\frac{1}{2}}$ .

$\frac{(a b - (b^{\frac{1}{2}} b) a^{\frac{1}{2}}) b^{\frac{1}{2}} - a {(b a)}^{\frac{1}{2}} a^{\frac{1}{2}} + b^{\frac{1}{2}} a (a^{\frac{1}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.3.4.2

Multiplique $b^{\frac{1}{2}}$ por $b$ .

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Etapa 4.3.4.2.1

Eleve $b$ à potência de $1$ .

$\frac{(a b - (b^{\frac{1}{2}} b^{1}) a^{\frac{1}{2}}) b^{\frac{1}{2}} - a {(b a)}^{\frac{1}{2}} a^{\frac{1}{2}} + b^{\frac{1}{2}} a (a^{\frac{1}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.3.4.2.2

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$\frac{(a b - b^{\frac{1}{2} + 1} a^{\frac{1}{2}}) b^{\frac{1}{2}} - a {(b a)}^{\frac{1}{2}} a^{\frac{1}{2}} + b^{\frac{1}{2}} a (a^{\frac{1}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.3.4.3

Escreva $1$ como uma fração com um denominador comum.

$\frac{(a b - b^{\frac{1}{2} + \frac{2}{2}} a^{\frac{1}{2}}) b^{\frac{1}{2}} - a {(b a)}^{\frac{1}{2}} a^{\frac{1}{2}} + b^{\frac{1}{2}} a (a^{\frac{1}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.3.4.4

Combine os numeradores em relação ao denominador comum.

$\frac{(a b - b^{\frac{1 + 2}{2}} a^{\frac{1}{2}}) b^{\frac{1}{2}} - a {(b a)}^{\frac{1}{2}} a^{\frac{1}{2}} + b^{\frac{1}{2}} a (a^{\frac{1}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.3.4.5

Some $1$ e $2$ .

$\frac{(a b - b^{\frac{3}{2}} a^{\frac{1}{2}}) b^{\frac{1}{2}} - a {(b a)}^{\frac{1}{2}} a^{\frac{1}{2}} + b^{\frac{1}{2}} a (a^{\frac{1}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.4

Aplique a propriedade distributiva.

$\frac{a b \cdot b^{\frac{1}{2}} - b^{\frac{3}{2}} a^{\frac{1}{2}} b^{\frac{1}{2}} - a {(b a)}^{\frac{1}{2}} a^{\frac{1}{2}} + b^{\frac{1}{2}} a (a^{\frac{1}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.5

Multiplique $b$ por $b^{\frac{1}{2}}$ somando os expoentes.

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Etapa 4.5.1

Mova $b^{\frac{1}{2}}$ .

$\frac{a (b^{\frac{1}{2}} b) - b^{\frac{3}{2}} a^{\frac{1}{2}} b^{\frac{1}{2}} - a {(b a)}^{\frac{1}{2}} a^{\frac{1}{2}} + b^{\frac{1}{2}} a (a^{\frac{1}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.5.2

Multiplique $b^{\frac{1}{2}}$ por $b$ .

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Etapa 4.5.2.1

Eleve $b$ à potência de $1$ .

$\frac{a (b^{\frac{1}{2}} b^{1}) - b^{\frac{3}{2}} a^{\frac{1}{2}} b^{\frac{1}{2}} - a {(b a)}^{\frac{1}{2}} a^{\frac{1}{2}} + b^{\frac{1}{2}} a (a^{\frac{1}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.5.2.2

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$\frac{a b^{\frac{1}{2} + 1} - b^{\frac{3}{2}} a^{\frac{1}{2}} b^{\frac{1}{2}} - a {(b a)}^{\frac{1}{2}} a^{\frac{1}{2}} + b^{\frac{1}{2}} a (a^{\frac{1}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.5.3

Escreva $1$ como uma fração com um denominador comum.

$\frac{a b^{\frac{1}{2} + \frac{2}{2}} - b^{\frac{3}{2}} a^{\frac{1}{2}} b^{\frac{1}{2}} - a {(b a)}^{\frac{1}{2}} a^{\frac{1}{2}} + b^{\frac{1}{2}} a (a^{\frac{1}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.5.4

Combine os numeradores em relação ao denominador comum.

$\frac{a b^{\frac{1 + 2}{2}} - b^{\frac{3}{2}} a^{\frac{1}{2}} b^{\frac{1}{2}} - a {(b a)}^{\frac{1}{2}} a^{\frac{1}{2}} + b^{\frac{1}{2}} a (a^{\frac{1}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.5.5

Some $1$ e $2$ .

$\frac{a b^{\frac{3}{2}} - b^{\frac{3}{2}} a^{\frac{1}{2}} b^{\frac{1}{2}} - a {(b a)}^{\frac{1}{2}} a^{\frac{1}{2}} + b^{\frac{1}{2}} a (a^{\frac{1}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.6

Multiplique $b^{\frac{3}{2}}$ por $b^{\frac{1}{2}}$ somando os expoentes.

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Etapa 4.6.1

Mova $b^{\frac{1}{2}}$ .

$\frac{a b^{\frac{3}{2}} - (b^{\frac{1}{2}} b^{\frac{3}{2}}) a^{\frac{1}{2}} - a {(b a)}^{\frac{1}{2}} a^{\frac{1}{2}} + b^{\frac{1}{2}} a (a^{\frac{1}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.6.2

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$\frac{a b^{\frac{3}{2}} - b^{\frac{1}{2} + \frac{3}{2}} a^{\frac{1}{2}} - a {(b a)}^{\frac{1}{2}} a^{\frac{1}{2}} + b^{\frac{1}{2}} a (a^{\frac{1}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.6.3

Combine os numeradores em relação ao denominador comum.

$\frac{a b^{\frac{3}{2}} - b^{\frac{1 + 3}{2}} a^{\frac{1}{2}} - a {(b a)}^{\frac{1}{2}} a^{\frac{1}{2}} + b^{\frac{1}{2}} a (a^{\frac{1}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.6.4

Some $1$ e $3$ .

$\frac{a b^{\frac{3}{2}} - b^{\frac{4}{2}} a^{\frac{1}{2}} - a {(b a)}^{\frac{1}{2}} a^{\frac{1}{2}} + b^{\frac{1}{2}} a (a^{\frac{1}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.6.5

Divida $4$ por $2$ .

$\frac{a b^{\frac{3}{2}} - b^{2} a^{\frac{1}{2}} - a {(b a)}^{\frac{1}{2}} a^{\frac{1}{2}} + b^{\frac{1}{2}} a (a^{\frac{1}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.7

Multiplique $a$ por $a^{\frac{1}{2}}$ somando os expoentes.

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Etapa 4.7.1

Mova $a^{\frac{1}{2}}$ .

$\frac{a b^{\frac{3}{2}} - b^{2} a^{\frac{1}{2}} - (a^{\frac{1}{2}} a) {(b a)}^{\frac{1}{2}} + b^{\frac{1}{2}} a (a^{\frac{1}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.7.2

Multiplique $a^{\frac{1}{2}}$ por $a$ .

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Etapa 4.7.2.1

Eleve $a$ à potência de $1$ .

$\frac{a b^{\frac{3}{2}} - b^{2} a^{\frac{1}{2}} - (a^{\frac{1}{2}} a^{1}) {(b a)}^{\frac{1}{2}} + b^{\frac{1}{2}} a (a^{\frac{1}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.7.2.2

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$\frac{a b^{\frac{3}{2}} - b^{2} a^{\frac{1}{2}} - a^{\frac{1}{2} + 1} {(b a)}^{\frac{1}{2}} + b^{\frac{1}{2}} a (a^{\frac{1}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.7.3

Escreva $1$ como uma fração com um denominador comum.

$\frac{a b^{\frac{3}{2}} - b^{2} a^{\frac{1}{2}} - a^{\frac{1}{2} + \frac{2}{2}} {(b a)}^{\frac{1}{2}} + b^{\frac{1}{2}} a (a^{\frac{1}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.7.4

Combine os numeradores em relação ao denominador comum.

$\frac{a b^{\frac{3}{2}} - b^{2} a^{\frac{1}{2}} - a^{\frac{1 + 2}{2}} {(b a)}^{\frac{1}{2}} + b^{\frac{1}{2}} a (a^{\frac{1}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.7.5

Some $1$ e $2$ .

$\frac{a b^{\frac{3}{2}} - b^{2} a^{\frac{1}{2}} - a^{\frac{3}{2}} {(b a)}^{\frac{1}{2}} + b^{\frac{1}{2}} a (a^{\frac{1}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.8

Aplique a regra do produto a $b a$ .

$\frac{a b^{\frac{3}{2}} - b^{2} a^{\frac{1}{2}} - a^{\frac{3}{2}} (b^{\frac{1}{2}} a^{\frac{1}{2}}) + b^{\frac{1}{2}} a (a^{\frac{1}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.9

Multiplique $a^{\frac{3}{2}}$ por $a^{\frac{1}{2}}$ somando os expoentes.

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Etapa 4.9.1

Mova $a^{\frac{1}{2}}$ .

$\frac{a b^{\frac{3}{2}} - b^{2} a^{\frac{1}{2}} - (a^{\frac{1}{2}} a^{\frac{3}{2}}) b^{\frac{1}{2}} + b^{\frac{1}{2}} a (a^{\frac{1}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.9.2

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$\frac{a b^{\frac{3}{2}} - b^{2} a^{\frac{1}{2}} - a^{\frac{1}{2} + \frac{3}{2}} b^{\frac{1}{2}} + b^{\frac{1}{2}} a (a^{\frac{1}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.9.3

Combine os numeradores em relação ao denominador comum.

$\frac{a b^{\frac{3}{2}} - b^{2} a^{\frac{1}{2}} - a^{\frac{1 + 3}{2}} b^{\frac{1}{2}} + b^{\frac{1}{2}} a (a^{\frac{1}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.9.4

Some $1$ e $3$ .

$\frac{a b^{\frac{3}{2}} - b^{2} a^{\frac{1}{2}} - a^{\frac{4}{2}} b^{\frac{1}{2}} + b^{\frac{1}{2}} a (a^{\frac{1}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.9.5

Divida $4$ por $2$ .

$\frac{a b^{\frac{3}{2}} - b^{2} a^{\frac{1}{2}} - a^{2} b^{\frac{1}{2}} + b^{\frac{1}{2}} a (a^{\frac{1}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.10

Multiplique $b^{\frac{1}{2}}$ por $b^{\frac{1}{2}}$ somando os expoentes.

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Etapa 4.10.1

Mova $b^{\frac{1}{2}}$ .

$\frac{a b^{\frac{3}{2}} - b^{2} a^{\frac{1}{2}} - a^{2} b^{\frac{1}{2}} + b^{\frac{1}{2}} b^{\frac{1}{2}} a \cdot a^{\frac{1}{2}}}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.10.2

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$\frac{a b^{\frac{3}{2}} - b^{2} a^{\frac{1}{2}} - a^{2} b^{\frac{1}{2}} + b^{\frac{1}{2} + \frac{1}{2}} a \cdot a^{\frac{1}{2}}}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.10.3

Combine os numeradores em relação ao denominador comum.

$\frac{a b^{\frac{3}{2}} - b^{2} a^{\frac{1}{2}} - a^{2} b^{\frac{1}{2}} + b^{\frac{1 + 1}{2}} a \cdot a^{\frac{1}{2}}}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.10.4

Some $1$ e $1$ .

$\frac{a b^{\frac{3}{2}} - b^{2} a^{\frac{1}{2}} - a^{2} b^{\frac{1}{2}} + b^{\frac{2}{2}} a \cdot a^{\frac{1}{2}}}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.10.5

Divida $2$ por $2$ .

$\frac{a b^{\frac{3}{2}} - b^{2} a^{\frac{1}{2}} - a^{2} b^{\frac{1}{2}} + b^{1} a \cdot a^{\frac{1}{2}}}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.11

Simplifique $b^{1} a \cdot a^{\frac{1}{2}}$ .

$\frac{a b^{\frac{3}{2}} - b^{2} a^{\frac{1}{2}} - a^{2} b^{\frac{1}{2}} + b a \cdot a^{\frac{1}{2}}}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.12

Multiplique $a$ por $a^{\frac{1}{2}}$ somando os expoentes.

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Etapa 4.12.1

Mova $a^{\frac{1}{2}}$ .

$\frac{a b^{\frac{3}{2}} - b^{2} a^{\frac{1}{2}} - a^{2} b^{\frac{1}{2}} + b (a^{\frac{1}{2}} a)}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.12.2

Multiplique $a^{\frac{1}{2}}$ por $a$ .

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Etapa 4.12.2.1

Eleve $a$ à potência de $1$ .

$\frac{a b^{\frac{3}{2}} - b^{2} a^{\frac{1}{2}} - a^{2} b^{\frac{1}{2}} + b (a^{\frac{1}{2}} a^{1})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.12.2.2

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$\frac{a b^{\frac{3}{2}} - b^{2} a^{\frac{1}{2}} - a^{2} b^{\frac{1}{2}} + b a^{\frac{1}{2} + 1}}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.12.3

Escreva $1$ como uma fração com um denominador comum.

$\frac{a b^{\frac{3}{2}} - b^{2} a^{\frac{1}{2}} - a^{2} b^{\frac{1}{2}} + b a^{\frac{1}{2} + \frac{2}{2}}}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.12.4

Combine os numeradores em relação ao denominador comum.

$\frac{a b^{\frac{3}{2}} - b^{2} a^{\frac{1}{2}} - a^{2} b^{\frac{1}{2}} + b a^{\frac{1 + 2}{2}}}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.12.5

Some $1$ e $2$ .

$\frac{a b^{\frac{3}{2}} - b^{2} a^{\frac{1}{2}} - a^{2} b^{\frac{1}{2}} + b a^{\frac{3}{2}}}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.13

Reescreva $a b^{\frac{3}{2}} - b^{2} a^{\frac{1}{2}} - a^{2} b^{\frac{1}{2}} + b a^{\frac{3}{2}}$ em uma forma fatorada.

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Etapa 4.13.1

Fatore $a^{\frac{1}{2}} b^{\frac{1}{2}}$ de $a b^{\frac{3}{2}} - b^{2} a^{\frac{1}{2}} - a^{2} b^{\frac{1}{2}} + b a^{\frac{3}{2}}$ .

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Etapa 4.13.1.1

Reordene a expressão.

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Etapa 4.13.1.1.1

Mova $b^{2}$ .

$\frac{a b^{\frac{3}{2}} - a^{\frac{1}{2}} b^{2} - a^{2} b^{\frac{1}{2}} + b a^{\frac{3}{2}}}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.13.1.1.2

Reordene $b$ e $a^{\frac{3}{2}}$ .

$\frac{a b^{\frac{3}{2}} - a^{\frac{1}{2}} b^{2} - a^{2} b^{\frac{1}{2}} + a^{\frac{3}{2}} b}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.13.1.2

Fatore $a^{\frac{1}{2}} b^{\frac{1}{2}}$ de $a b^{\frac{3}{2}}$ .

$\frac{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} b^{\frac{2}{2}}) - a^{\frac{1}{2}} b^{2} - a^{2} b^{\frac{1}{2}} + a^{\frac{3}{2}} b}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.13.1.3

Fatore $a^{\frac{1}{2}} b^{\frac{1}{2}}$ de $- a^{\frac{1}{2}} b^{2}$ .

$\frac{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} b^{\frac{2}{2}}) + a^{\frac{1}{2}} b^{\frac{1}{2}} (- b^{\frac{3}{2}}) - a^{2} b^{\frac{1}{2}} + a^{\frac{3}{2}} b}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.13.1.4

Fatore $a^{\frac{1}{2}} b^{\frac{1}{2}}$ de $- a^{2} b^{\frac{1}{2}}$ .

$\frac{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} b^{\frac{2}{2}}) + a^{\frac{1}{2}} b^{\frac{1}{2}} (- b^{\frac{3}{2}}) + a^{\frac{1}{2}} b^{\frac{1}{2}} (- a^{\frac{3}{2}}) + a^{\frac{3}{2}} b}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.13.1.5

Fatore $a^{\frac{1}{2}} b^{\frac{1}{2}}$ de $a^{\frac{3}{2}} b$ .

$\frac{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} b^{\frac{2}{2}}) + a^{\frac{1}{2}} b^{\frac{1}{2}} (- b^{\frac{3}{2}}) + a^{\frac{1}{2}} b^{\frac{1}{2}} (- a^{\frac{3}{2}}) + a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{2}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.13.1.6

Fatore $a^{\frac{1}{2}} b^{\frac{1}{2}}$ de $a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} b^{\frac{2}{2}}) + a^{\frac{1}{2}} b^{\frac{1}{2}} (- b^{\frac{3}{2}})$ .

$\frac{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} b^{\frac{2}{2}} - b^{\frac{3}{2}}) + a^{\frac{1}{2}} b^{\frac{1}{2}} (- a^{\frac{3}{2}}) + a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{2}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.13.1.7

Fatore $a^{\frac{1}{2}} b^{\frac{1}{2}}$ de $a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} b^{\frac{2}{2}} - b^{\frac{3}{2}}) + a^{\frac{1}{2}} b^{\frac{1}{2}} (- a^{\frac{3}{2}})$ .

$\frac{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} b^{\frac{2}{2}} - b^{\frac{3}{2}} - a^{\frac{3}{2}}) + a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{2}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.13.1.8

Fatore $a^{\frac{1}{2}} b^{\frac{1}{2}}$ de $a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} b^{\frac{2}{2}} - b^{\frac{3}{2}} - a^{\frac{3}{2}}) + a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{2}{2}} b^{\frac{1}{2}})$ .

$\frac{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} b^{\frac{2}{2}} - b^{\frac{3}{2}} - a^{\frac{3}{2}} + a^{\frac{2}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.13.2

Reagrupe os termos.

$\frac{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} b^{\frac{2}{2}} + a^{\frac{2}{2}} b^{\frac{1}{2}} - b^{\frac{3}{2}} - a^{\frac{3}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.13.3

Fatore $a^{\frac{1}{2}} b^{\frac{1}{2}}$ de $a^{\frac{1}{2}} b^{\frac{2}{2}} + a^{\frac{2}{2}} b^{\frac{1}{2}}$ .

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Etapa 4.13.3.1

Fatore $a^{\frac{1}{2}} b^{\frac{1}{2}}$ de $a^{\frac{1}{2}} b^{\frac{2}{2}}$ .

$\frac{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} b^{\frac{1}{2}} (b^{\frac{1}{2}}) + a^{\frac{2}{2}} b^{\frac{1}{2}} - b^{\frac{3}{2}} - a^{\frac{3}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.13.3.2

Fatore $a^{\frac{1}{2}} b^{\frac{1}{2}}$ de $a^{\frac{2}{2}} b^{\frac{1}{2}}$ .

$\frac{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} b^{\frac{1}{2}} (b^{\frac{1}{2}}) + a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}}) - b^{\frac{3}{2}} - a^{\frac{3}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.13.3.3

Fatore $a^{\frac{1}{2}} b^{\frac{1}{2}}$ de $a^{\frac{1}{2}} b^{\frac{1}{2}} (b^{\frac{1}{2}}) + a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}})$ .

$\frac{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} b^{\frac{1}{2}} (b^{\frac{1}{2}} + a^{\frac{1}{2}}) - b^{\frac{3}{2}} - a^{\frac{3}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.13.4

Fatore $- 1$ de $- b^{\frac{3}{2}} - a^{\frac{3}{2}}$ .

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Etapa 4.13.4.1

Fatore $- 1$ de $- b^{\frac{3}{2}}$ .

$\frac{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} b^{\frac{1}{2}} (b^{\frac{1}{2}} + a^{\frac{1}{2}}) - (b^{\frac{3}{2}}) - a^{\frac{3}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.13.4.2

Fatore $- 1$ de $- a^{\frac{3}{2}}$ .

$\frac{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} b^{\frac{1}{2}} (b^{\frac{1}{2}} + a^{\frac{1}{2}}) - (b^{\frac{3}{2}}) - (a^{\frac{3}{2}}))}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.13.4.3

Fatore $- 1$ de $- (b^{\frac{3}{2}}) - (a^{\frac{3}{2}})$ .

$\frac{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} b^{\frac{1}{2}} (b^{\frac{1}{2}} + a^{\frac{1}{2}}) - (b^{\frac{3}{2}} + a^{\frac{3}{2}}))}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.13.5

Reescreva $b^{\frac{3}{2}}$ como ${(b^{\frac{1}{2}})}^{3}$ .

$\frac{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} b^{\frac{1}{2}} (b^{\frac{1}{2}} + a^{\frac{1}{2}}) - ({(b^{\frac{1}{2}})}^{3} + a^{\frac{3}{2}}))}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.13.6

Reescreva $a^{\frac{3}{2}}$ como ${(a^{\frac{1}{2}})}^{3}$ .

$\frac{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} b^{\frac{1}{2}} (b^{\frac{1}{2}} + a^{\frac{1}{2}}) - ({(b^{\frac{1}{2}})}^{3} + {(a^{\frac{1}{2}})}^{3}))}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.13.7

Como os dois termos são cubos perfeitos, fatore usando a fórmula da soma de cubos, $a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$ em que $a = b^{\frac{1}{2}}$ e $b = a^{\frac{1}{2}}$ .

$\frac{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} b^{\frac{1}{2}} (b^{\frac{1}{2}} + a^{\frac{1}{2}}) - ((b^{\frac{1}{2}} + a^{\frac{1}{2}}) ({(b^{\frac{1}{2}})}^{2} - b^{\frac{1}{2}} a^{\frac{1}{2}} + {(a^{\frac{1}{2}})}^{2})))}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.13.8

Simplifique.

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Etapa 4.13.8.1

Multiplique os expoentes em ${(b^{\frac{1}{2}})}^{2}$ .

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Etapa 4.13.8.1.1

Aplique a regra da multiplicação de potências e multiplique os expoentes, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} b^{\frac{1}{2}} (b^{\frac{1}{2}} + a^{\frac{1}{2}}) - ((b^{\frac{1}{2}} + a^{\frac{1}{2}}) (b^{\frac{1}{2} \cdot 2} - b^{\frac{1}{2}} a^{\frac{1}{2}} + {(a^{\frac{1}{2}})}^{2})))}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.13.8.1.2

Cancele o fator comum de $2$ .

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Etapa 4.13.8.1.2.1

Cancele o fator comum.

Etapa 4.13.8.1.2.2

Reescreva a expressão.

$\frac{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} b^{\frac{1}{2}} (b^{\frac{1}{2}} + a^{\frac{1}{2}}) - ((b^{\frac{1}{2}} + a^{\frac{1}{2}}) (b^{1} - b^{\frac{1}{2}} a^{\frac{1}{2}} + {(a^{\frac{1}{2}})}^{2})))}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.13.8.2

Simplifique.

$\frac{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} b^{\frac{1}{2}} (b^{\frac{1}{2}} + a^{\frac{1}{2}}) - ((b^{\frac{1}{2}} + a^{\frac{1}{2}}) (b - b^{\frac{1}{2}} a^{\frac{1}{2}} + {(a^{\frac{1}{2}})}^{2})))}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.13.8.3

Multiplique os expoentes em ${(a^{\frac{1}{2}})}^{2}$ .

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Etapa 4.13.8.3.1

Aplique a regra da multiplicação de potências e multiplique os expoentes, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} b^{\frac{1}{2}} (b^{\frac{1}{2}} + a^{\frac{1}{2}}) - ((b^{\frac{1}{2}} + a^{\frac{1}{2}}) (b - b^{\frac{1}{2}} a^{\frac{1}{2}} + a^{\frac{1}{2} \cdot 2})))}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.13.8.3.2

Cancele o fator comum de $2$ .

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Etapa 4.13.8.3.2.1

Cancele o fator comum.

$\frac{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} b^{\frac{1}{2}} (b^{\frac{1}{2}} + a^{\frac{1}{2}}) - ((b^{\frac{1}{2}} + a^{\frac{1}{2}}) (b - b^{\frac{1}{2}} a^{\frac{1}{2}} + a^{\frac{1}{2} \cdot 2})))}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.13.8.3.2.2

Reescreva a expressão.

$\frac{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} b^{\frac{1}{2}} (b^{\frac{1}{2}} + a^{\frac{1}{2}}) - ((b^{\frac{1}{2}} + a^{\frac{1}{2}}) (b - b^{\frac{1}{2}} a^{\frac{1}{2}} + a^{1})))}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.13.8.4

Simplifique.

$\frac{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} b^{\frac{1}{2}} (b^{\frac{1}{2}} + a^{\frac{1}{2}}) - ((b^{\frac{1}{2}} + a^{\frac{1}{2}}) (b - b^{\frac{1}{2}} a^{\frac{1}{2}} + a)))}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

$\frac{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} b^{\frac{1}{2}} (b^{\frac{1}{2}} + a^{\frac{1}{2}}) - (b^{\frac{1}{2}} + a^{\frac{1}{2}}) (b - b^{\frac{1}{2}} a^{\frac{1}{2}} + a))}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.13.9

Fatore $b^{\frac{1}{2}} + a^{\frac{1}{2}}$ de $a^{\frac{1}{2}} b^{\frac{1}{2}} (b^{\frac{1}{2}} + a^{\frac{1}{2}}) - (b^{\frac{1}{2}} + a^{\frac{1}{2}}) (b - b^{\frac{1}{2}} a^{\frac{1}{2}} + a)$ .

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Etapa 4.13.9.1

Reordene a expressão.

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Etapa 4.13.9.1.1

Mova $b^{\frac{1}{2}}$ .

$\frac{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} b^{\frac{1}{2}} (b^{\frac{1}{2}} + a^{\frac{1}{2}}) - (b^{\frac{1}{2}} + a^{\frac{1}{2}}) (b - 1 a^{\frac{1}{2}} b^{\frac{1}{2}} + a))}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.13.9.1.2

Mova $- 1 a^{\frac{1}{2}} b^{\frac{1}{2}}$ .

$\frac{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} b^{\frac{1}{2}} (b^{\frac{1}{2}} + a^{\frac{1}{2}}) - (b^{\frac{1}{2}} + a^{\frac{1}{2}}) (b + a - 1 a^{\frac{1}{2}} b^{\frac{1}{2}}))}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.13.9.1.3

Reordene $b$ e $a$ .

$\frac{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} b^{\frac{1}{2}} (b^{\frac{1}{2}} + a^{\frac{1}{2}}) - (b^{\frac{1}{2}} + a^{\frac{1}{2}}) (a + b - 1 a^{\frac{1}{2}} b^{\frac{1}{2}}))}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.13.9.2

Fatore $b^{\frac{1}{2}} + a^{\frac{1}{2}}$ de $a^{\frac{1}{2}} b^{\frac{1}{2}} (b^{\frac{1}{2}} + a^{\frac{1}{2}})$ .

$\frac{a^{\frac{1}{2}} b^{\frac{1}{2}} ((b^{\frac{1}{2}} + a^{\frac{1}{2}}) (a^{\frac{1}{2}} b^{\frac{1}{2}}) - (b^{\frac{1}{2}} + a^{\frac{1}{2}}) (a + b - 1 a^{\frac{1}{2}} b^{\frac{1}{2}}))}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.13.9.3

Fatore $b^{\frac{1}{2}} + a^{\frac{1}{2}}$ de $- (b^{\frac{1}{2}} + a^{\frac{1}{2}}) (a + b - 1 a^{\frac{1}{2}} b^{\frac{1}{2}})$ .

$\frac{a^{\frac{1}{2}} b^{\frac{1}{2}} ((b^{\frac{1}{2}} + a^{\frac{1}{2}}) (a^{\frac{1}{2}} b^{\frac{1}{2}}) + (b^{\frac{1}{2}} + a^{\frac{1}{2}}) (- 1 (a + b - 1 a^{\frac{1}{2}} b^{\frac{1}{2}})))}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.13.9.4

Fatore $b^{\frac{1}{2}} + a^{\frac{1}{2}}$ de $(b^{\frac{1}{2}} + a^{\frac{1}{2}}) (a^{\frac{1}{2}} b^{\frac{1}{2}}) + (b^{\frac{1}{2}} + a^{\frac{1}{2}}) (- 1 (a + b - 1 a^{\frac{1}{2}} b^{\frac{1}{2}}))$ .

$\frac{a^{\frac{1}{2}} b^{\frac{1}{2}} ((b^{\frac{1}{2}} + a^{\frac{1}{2}}) (a^{\frac{1}{2}} b^{\frac{1}{2}} - 1 (a + b - 1 a^{\frac{1}{2}} b^{\frac{1}{2}})))}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.13.10

Reescreva $- 1 a^{\frac{1}{2}}$ como $- a^{\frac{1}{2}}$ .

$\frac{a^{\frac{1}{2}} b^{\frac{1}{2}} ((b^{\frac{1}{2}} + a^{\frac{1}{2}}) (a^{\frac{1}{2}} b^{\frac{1}{2}} - 1 (a + b - a^{\frac{1}{2}} b^{\frac{1}{2}})))}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.13.11

Aplique a propriedade distributiva.

$\frac{a^{\frac{1}{2}} b^{\frac{1}{2}} ((b^{\frac{1}{2}} + a^{\frac{1}{2}}) (a^{\frac{1}{2}} b^{\frac{1}{2}} - 1 a - 1 b - 1 (- a^{\frac{1}{2}} b^{\frac{1}{2}})))}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.13.12

Simplifique.

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Etapa 4.13.12.1

Reescreva $- 1 a$ como $- a$ .

$\frac{a^{\frac{1}{2}} b^{\frac{1}{2}} ((b^{\frac{1}{2}} + a^{\frac{1}{2}}) (a^{\frac{1}{2}} b^{\frac{1}{2}} - a - 1 b - 1 (- a^{\frac{1}{2}} b^{\frac{1}{2}})))}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.13.12.2

Reescreva $- 1 b$ como $- b$ .

$\frac{a^{\frac{1}{2}} b^{\frac{1}{2}} ((b^{\frac{1}{2}} + a^{\frac{1}{2}}) (a^{\frac{1}{2}} b^{\frac{1}{2}} - a - b - 1 (- a^{\frac{1}{2}} b^{\frac{1}{2}})))}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.13.12.3

Multiplique $- 1 (- a^{\frac{1}{2}} b^{\frac{1}{2}})$ .

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Etapa 4.13.12.3.1

Multiplique $- 1$ por $- 1$ .

$\frac{a^{\frac{1}{2}} b^{\frac{1}{2}} ((b^{\frac{1}{2}} + a^{\frac{1}{2}}) (a^{\frac{1}{2}} b^{\frac{1}{2}} - a - b + 1 (a^{\frac{1}{2}} b^{\frac{1}{2}})))}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.13.12.3.2

Multiplique $a^{\frac{1}{2}}$ por $1$ .

$\frac{a^{\frac{1}{2}} b^{\frac{1}{2}} ((b^{\frac{1}{2}} + a^{\frac{1}{2}}) (a^{\frac{1}{2}} b^{\frac{1}{2}} - a - b + a^{\frac{1}{2}} b^{\frac{1}{2}}))}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 4.13.13

Some $a^{\frac{1}{2}} b^{\frac{1}{2}}$ e $a^{\frac{1}{2}} b^{\frac{1}{2}}$ .

$\frac{a^{\frac{1}{2}} b^{\frac{1}{2}} (b^{\frac{1}{2}} + a^{\frac{1}{2}}) (- a - b + 2 a^{\frac{1}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 5

Simplifique os termos.

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Etapa 5.1

Cancele o fator comum.

$\frac{a^{\frac{1}{2}} b^{\frac{1}{2}} (b^{\frac{1}{2}} + a^{\frac{1}{2}}) (- a - b + 2 a^{\frac{1}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 5.2

Reescreva a expressão.

$\frac{(b^{\frac{1}{2}} (b^{\frac{1}{2}} + a^{\frac{1}{2}})) (- a - b + 2 a^{\frac{1}{2}} b^{\frac{1}{2}})}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 5.3

Cancele o fator comum.

$\frac{b^{\frac{1}{2}} (b^{\frac{1}{2}} + a^{\frac{1}{2}}) (- a - b + 2 a^{\frac{1}{2}} b^{\frac{1}{2}})}{b^{\frac{1}{2}} (a^{\frac{1}{2}} - b^{\frac{1}{2}})}$

Etapa 5.4

Reescreva a expressão.

$\frac{(b^{\frac{1}{2}} + a^{\frac{1}{2}}) (- a - b + 2 a^{\frac{1}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} - b^{\frac{1}{2}}}$

Etapa 5.5

Fatore $- 1$ de $- a$ .

$\frac{(b^{\frac{1}{2}} + a^{\frac{1}{2}}) (- (a) - b + 2 a^{\frac{1}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} - b^{\frac{1}{2}}}$

Etapa 5.6

Fatore $- 1$ de $- b$ .

$\frac{(b^{\frac{1}{2}} + a^{\frac{1}{2}}) (- (a) - (b) + 2 a^{\frac{1}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} - b^{\frac{1}{2}}}$

Etapa 5.7

Fatore $- 1$ de $- (a) - (b)$ .

$\frac{(b^{\frac{1}{2}} + a^{\frac{1}{2}}) (- (a + b) + 2 a^{\frac{1}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} - b^{\frac{1}{2}}}$

Etapa 5.8

Fatore $- 1$ de $2 a^{\frac{1}{2}} b^{\frac{1}{2}}$ .

$\frac{(b^{\frac{1}{2}} + a^{\frac{1}{2}}) (- (a + b) - (- 2 a^{\frac{1}{2}} b^{\frac{1}{2}}))}{a^{\frac{1}{2}} - b^{\frac{1}{2}}}$

Etapa 5.9

Fatore $- 1$ de $- (a + b) - (- 2 a^{\frac{1}{2}} b^{\frac{1}{2}})$ .

$\frac{(b^{\frac{1}{2}} + a^{\frac{1}{2}}) (- (a + b - 2 a^{\frac{1}{2}} b^{\frac{1}{2}}))}{a^{\frac{1}{2}} - b^{\frac{1}{2}}}$

Etapa 5.10

Simplifique a expressão.

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Etapa 5.10.1

Reescreva $- (a + b - 2 a^{\frac{1}{2}} b^{\frac{1}{2}})$ como $- 1 (a + b - 2 a^{\frac{1}{2}} b^{\frac{1}{2}})$ .

$\frac{(b^{\frac{1}{2}} + a^{\frac{1}{2}}) (- 1 (a + b - 2 a^{\frac{1}{2}} b^{\frac{1}{2}}))}{a^{\frac{1}{2}} - b^{\frac{1}{2}}}$

Etapa 5.10.2

Mova o número negativo para a frente da fração.

$- \frac{(b^{\frac{1}{2}} + a^{\frac{1}{2}}) (a + b - 2 a^{\frac{1}{2}} b^{\frac{1}{2}})}{a^{\frac{1}{2}} - b^{\frac{1}{2}}}$