Matemática básica Exemplos

\frac{\sqrt{y}}{\sqrt{13} + \sqrt{11}} \cdot \frac{\sqrt{13} - \sqrt{11}}{\sqrt{13} - \sqrt{11}}

$\frac{\sqrt{y}}{\sqrt{13} + \sqrt{11}} \cdot \frac{\sqrt{13} - \sqrt{11}}{\sqrt{13} - \sqrt{11}}$

Etapa 1

Multiplique

\frac{\sqrt{y}}{\sqrt{13} + \sqrt{11}}

$\frac{\sqrt{y}}{\sqrt{13} + \sqrt{11}}$ por

\frac{\sqrt{13} - \sqrt{11}}{\sqrt{13} - \sqrt{11}}

$\frac{\sqrt{13} - \sqrt{11}}{\sqrt{13} - \sqrt{11}}$ .

\frac{\sqrt{y}}{\sqrt{13} + \sqrt{11}} \cdot \frac{\sqrt{13} - \sqrt{11}}{\sqrt{13} - \sqrt{11}} \cdot \frac{\sqrt{13} - \sqrt{11}}{\sqrt{13} - \sqrt{11}}

$\frac{\sqrt{y}}{\sqrt{13} + \sqrt{11}} \cdot \frac{\sqrt{13} - \sqrt{11}}{\sqrt{13} - \sqrt{11}} \cdot \frac{\sqrt{13} - \sqrt{11}}{\sqrt{13} - \sqrt{11}}$

Etapa 2

Multiplique

\frac{\sqrt{y}}{\sqrt{13} + \sqrt{11}}

$\frac{\sqrt{y}}{\sqrt{13} + \sqrt{11}}$ por

\frac{\sqrt{13} - \sqrt{11}}{\sqrt{13} - \sqrt{11}}

$\frac{\sqrt{13} - \sqrt{11}}{\sqrt{13} - \sqrt{11}}$ .

\frac{\sqrt{y} (\sqrt{13} - \sqrt{11})}{(\sqrt{13} + \sqrt{11}) (\sqrt{13} - \sqrt{11})} \cdot \frac{\sqrt{13} - \sqrt{11}}{\sqrt{13} - \sqrt{11}}

$\frac{\sqrt{y} (\sqrt{13} - \sqrt{11})}{(\sqrt{13} + \sqrt{11}) (\sqrt{13} - \sqrt{11})} \cdot \frac{\sqrt{13} - \sqrt{11}}{\sqrt{13} - \sqrt{11}}$

Etapa 3

Expanda o denominador usando o método FOIL.

\frac{\sqrt{y} (\sqrt{13} - \sqrt{11})}{{\sqrt{13}}^{2} - \sqrt{143} + \sqrt{143} - {\sqrt{11}}^{2}} \cdot \frac{\sqrt{13} - \sqrt{11}}{\sqrt{13} - \sqrt{11}}

$\frac{\sqrt{y} (\sqrt{13} - \sqrt{11})}{{\sqrt{13}}^{2} - \sqrt{143} + \sqrt{143} - {\sqrt{11}}^{2}} \cdot \frac{\sqrt{13} - \sqrt{11}}{\sqrt{13} - \sqrt{11}}$

Etapa 4

Simplifique.

\frac{\sqrt{y} (\sqrt{13} - \sqrt{11})}{2} \cdot \frac{\sqrt{13} - \sqrt{11}}{\sqrt{13} - \sqrt{11}}

$\frac{\sqrt{y} (\sqrt{13} - \sqrt{11})}{2} \cdot \frac{\sqrt{13} - \sqrt{11}}{\sqrt{13} - \sqrt{11}}$

Etapa 5

Cancele o fator comum de

\sqrt{13} - \sqrt{11}

$\sqrt{13} - \sqrt{11}$ .

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Etapa 5.1

Fatore

\sqrt{13} - \sqrt{11}

$\sqrt{13} - \sqrt{11}$ de

\sqrt{y} (\sqrt{13} - \sqrt{11})

$\sqrt{y} (\sqrt{13} - \sqrt{11})$ .

\frac{(\sqrt{13} - \sqrt{11}) \sqrt{y}}{2} \cdot \frac{\sqrt{13} - \sqrt{11}}{\sqrt{13} - \sqrt{11}}

$\frac{(\sqrt{13} - \sqrt{11}) \sqrt{y}}{2} \cdot \frac{\sqrt{13} - \sqrt{11}}{\sqrt{13} - \sqrt{11}}$

Etapa 5.2

Cancele o fator comum.

\frac{(\sqrt{13} - \sqrt{11}) \sqrt{y}}{2} \cdot \frac{\sqrt{13} - \sqrt{11}}{\sqrt{13} - \sqrt{11}}

$\frac{(\sqrt{13} - \sqrt{11}) \sqrt{y}}{2} \cdot \frac{\sqrt{13} - \sqrt{11}}{\sqrt{13} - \sqrt{11}}$

Etapa 5.3

Reescreva a expressão.

\frac{\sqrt{y}}{2} \cdot (\sqrt{13} - \sqrt{11})

$\frac{\sqrt{y}}{2} \cdot (\sqrt{13} - \sqrt{11})$

\frac{\sqrt{y}}{2} \cdot (\sqrt{13} - \sqrt{11})

$\frac{\sqrt{y}}{2} \cdot (\sqrt{13} - \sqrt{11})$

Etapa 6

Aplique a propriedade distributiva.

\frac{\sqrt{y}}{2} \sqrt{13} + \frac{\sqrt{y}}{2} (- \sqrt{11})

$\frac{\sqrt{y}}{2} \sqrt{13} + \frac{\sqrt{y}}{2} (- \sqrt{11})$

Etapa 7

Multiplique

\frac{\sqrt{y}}{2} \sqrt{13}

$\frac{\sqrt{y}}{2} \sqrt{13}$ .

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Etapa 7.1

Combine

\frac{\sqrt{y}}{2}

$\frac{\sqrt{y}}{2}$ e

\sqrt{13}

$\sqrt{13}$ .

\frac{\sqrt{y} \sqrt{13}}{2} + \frac{\sqrt{y}}{2} (- \sqrt{11})

$\frac{\sqrt{y} \sqrt{13}}{2} + \frac{\sqrt{y}}{2} (- \sqrt{11})$

Etapa 7.2

Combine usando a regra do produto para radicais.

\frac{\sqrt{y \cdot 13}}{2} + \frac{\sqrt{y}}{2} (- \sqrt{11})

$\frac{\sqrt{y \cdot 13}}{2} + \frac{\sqrt{y}}{2} (- \sqrt{11})$

\frac{\sqrt{y \cdot 13}}{2} + \frac{\sqrt{y}}{2} (- \sqrt{11})

$\frac{\sqrt{y \cdot 13}}{2} + \frac{\sqrt{y}}{2} (- \sqrt{11})$

Etapa 8

Multiplique

\frac{\sqrt{y}}{2} (- \sqrt{11})

$\frac{\sqrt{y}}{2} (- \sqrt{11})$ .

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Etapa 8.1

Combine

\frac{\sqrt{y}}{2}

$\frac{\sqrt{y}}{2}$ e

\sqrt{11}

$\sqrt{11}$ .

\frac{\sqrt{y \cdot 13}}{2} - \frac{\sqrt{y} \sqrt{11}}{2}

$\frac{\sqrt{y \cdot 13}}{2} - \frac{\sqrt{y} \sqrt{11}}{2}$

Etapa 8.2

Combine usando a regra do produto para radicais.

\frac{\sqrt{y \cdot 13}}{2} - \frac{\sqrt{y \cdot 11}}{2}

$\frac{\sqrt{y \cdot 13}}{2} - \frac{\sqrt{y \cdot 11}}{2}$

\frac{\sqrt{y \cdot 13}}{2} - \frac{\sqrt{y \cdot 11}}{2}

$\frac{\sqrt{y \cdot 13}}{2} - \frac{\sqrt{y \cdot 11}}{2}$

Etapa 9

Reordene os fatores em

\frac{\sqrt{y \cdot 13}}{2} - \frac{\sqrt{y \cdot 11}}{2}

$\frac{\sqrt{y \cdot 13}}{2} - \frac{\sqrt{y \cdot 11}}{2}$ .

\frac{\sqrt{13 y}}{2} - \frac{\sqrt{11 y}}{2}

$\frac{\sqrt{13 y}}{2} - \frac{\sqrt{11 y}}{2}$