Pre-Algebra Examples

$- \frac{4}{\sqrt{x} - 5}$

Step 1

Multiply $\frac{4}{\sqrt{x} - 5}$ by $\frac{\sqrt{x} + 5}{\sqrt{x} + 5}$ .

$- (\frac{4}{\sqrt{x} - 5} \cdot \frac{\sqrt{x} + 5}{\sqrt{x} + 5})$

Step 2

Multiply $\frac{4}{\sqrt{x} - 5}$ by $\frac{\sqrt{x} + 5}{\sqrt{x} + 5}$ .

$- \frac{4 (\sqrt{x} + 5)}{(\sqrt{x} - 5) (\sqrt{x} + 5)}$

Step 3

Expand the denominator using the FOIL method.

$- \frac{4 (\sqrt{x} + 5)}{{\sqrt{x}}^{2} + \sqrt{x} \cdot 5 - 5 \sqrt{x} - 25}$

Step 4

Simplify.

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Step 4.1

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

$- \frac{4 (\sqrt{x} + 5)}{{(x^{\frac{1}{2}})}^{2} - 25}$

Step 4.2

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

$- \frac{4 (\sqrt{x} + 5)}{x^{\frac{1}{2} \cdot 2} - 25}$

Step 4.3

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

$- \frac{4 (\sqrt{x} + 5)}{x^{\frac{2}{2}} - 25}$

Step 4.4

Cancel the common factor of $2$ .

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Step 4.4.1

Cancel the common factor.

$- \frac{4 (\sqrt{x} + 5)}{x^{\frac{2}{2}} - 25}$

Step 4.4.2

Rewrite the expression.

$- \frac{4 (\sqrt{x} + 5)}{x^{1} - 25}$

Step 4.5

Simplify.

$- \frac{4 (\sqrt{x} + 5)}{x - 25}$