Precalculus Examples

$\frac{6 (x - y)}{\sqrt{x} - \sqrt{y}}$

Step 1

Multiply $\frac{6 (x - y)}{\sqrt{x} - \sqrt{y}}$ by $\frac{\sqrt{x} + \sqrt{y}}{\sqrt{x} + \sqrt{y}}$ .

$\frac{6 (x - y)}{\sqrt{x} - \sqrt{y}} \cdot \frac{\sqrt{x} + \sqrt{y}}{\sqrt{x} + \sqrt{y}}$

Step 2

Multiply $\frac{6 (x - y)}{\sqrt{x} - \sqrt{y}}$ by $\frac{\sqrt{x} + \sqrt{y}}{\sqrt{x} + \sqrt{y}}$ .

$\frac{6 (x - y) (\sqrt{x} + \sqrt{y})}{(\sqrt{x} - \sqrt{y}) (\sqrt{x} + \sqrt{y})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{6 (x - y) (\sqrt{x} + \sqrt{y})}{{\sqrt{x}}^{2} + \sqrt{x y} - \sqrt{x y} - {\sqrt{y}}^{2}}$

Step 4

Simplify.

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Step 4.1

Rewrite ${\sqrt{x}}^{2}$ as $x$ .

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Step 4.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x}$ as $x^{\frac{1}{2}}$ .

$\frac{6 (x - y) (\sqrt{x} + \sqrt{y})}{{(x^{\frac{1}{2}})}^{2} - {\sqrt{y}}^{2}}$

Step 4.1.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{6 (x - y) (\sqrt{x} + \sqrt{y})}{x^{\frac{1}{2} \cdot 2} - {\sqrt{y}}^{2}}$

Step 4.1.3

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

$\frac{6 (x - y) (\sqrt{x} + \sqrt{y})}{x^{\frac{2}{2}} - {\sqrt{y}}^{2}}$

Step 4.1.4

Cancel the common factor of $2$ .

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Step 4.1.4.1

Cancel the common factor.

$\frac{6 (x - y) (\sqrt{x} + \sqrt{y})}{x^{\frac{2}{2}} - {\sqrt{y}}^{2}}$

Step 4.1.4.2

Rewrite the expression.

$\frac{6 (x - y) (\sqrt{x} + \sqrt{y})}{x^{1} - {\sqrt{y}}^{2}}$

Step 4.1.5

Simplify.

$\frac{6 (x - y) (\sqrt{x} + \sqrt{y})}{x - {\sqrt{y}}^{2}}$

Step 4.2

Rewrite ${\sqrt{y}}^{2}$ as $y$ .

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Step 4.2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{y}$ as $y^{\frac{1}{2}}$ .

$\frac{6 (x - y) (\sqrt{x} + \sqrt{y})}{x - {(y^{\frac{1}{2}})}^{2}}$

Step 4.2.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{6 (x - y) (\sqrt{x} + \sqrt{y})}{x - y^{\frac{1}{2} \cdot 2}}$

Step 4.2.3

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

$\frac{6 (x - y) (\sqrt{x} + \sqrt{y})}{x - y^{\frac{2}{2}}}$

Step 4.2.4

Cancel the common factor of $2$ .

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Step 4.2.4.1

Cancel the common factor.

$\frac{6 (x - y) (\sqrt{x} + \sqrt{y})}{x - y^{\frac{2}{2}}}$

Step 4.2.4.2

Rewrite the expression.

$\frac{6 (x - y) (\sqrt{x} + \sqrt{y})}{x - y^{1}}$

Step 4.2.5

Simplify.

$\frac{6 (x - y) (\sqrt{x} + \sqrt{y})}{x - y}$

Step 5

Cancel the common factor of $x - y$ .

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Step 5.1

Cancel the common factor.

$\frac{6 (x - y) (\sqrt{x} + \sqrt{y})}{x - y}$

Step 5.2

Divide $6 (\sqrt{x} + \sqrt{y})$ by $1$ .

$6 (\sqrt{x} + \sqrt{y})$

Step 6

Apply the distributive property.

$6 \sqrt{x} + 6 \sqrt{y}$