Pre-Algebra Examples

$\frac{x}{4 + \sqrt{x}}$

Step 1

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

$\frac{x}{4 + \sqrt{x}} \cdot \frac{4 - \sqrt{x}}{4 - \sqrt{x}}$

Step 2

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

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

Step 3

Expand the denominator using the FOIL method.

$\frac{x (4 - \sqrt{x})}{16 - 4 \sqrt{x} + \sqrt{x} \cdot 4 - {\sqrt{x}}^{2}}$

Step 4

Simplify.

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Step 4.1

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

$\frac{x (4 - \sqrt{x})}{16 - {(x^{\frac{1}{2}})}^{2}}$

Step 4.2

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

$\frac{x (4 - \sqrt{x})}{16 - x^{\frac{1}{2} \cdot 2}}$

Step 4.3

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

$\frac{x (4 - \sqrt{x})}{16 - x^{\frac{2}{2}}}$

Step 4.4

Cancel the common factor of $2$ .

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Step 4.4.1

Cancel the common factor.

$\frac{x (4 - \sqrt{x})}{16 - x^{\frac{2}{2}}}$

Step 4.4.2

Rewrite the expression.

$\frac{x (4 - \sqrt{x})}{16 - x^{1}}$

Step 4.5

Simplify.

$\frac{x (4 - \sqrt{x})}{16 - x}$