Pre-Algebra Examples

$\frac{- 3}{5 - 2 \sqrt{x}}$

Step 1

Move the negative in front of the fraction.

$- \frac{3}{5 - 2 \sqrt{x}}$

Step 2

Multiply $\frac{3}{5 - 2 \sqrt{x}}$ by $\frac{5 + 2 \sqrt{x}}{5 + 2 \sqrt{x}}$ .

$- (\frac{3}{5 - 2 \sqrt{x}} \cdot \frac{5 + 2 \sqrt{x}}{5 + 2 \sqrt{x}})$

Step 3

Multiply $\frac{3}{5 - 2 \sqrt{x}}$ by $\frac{5 + 2 \sqrt{x}}{5 + 2 \sqrt{x}}$ .

$- \frac{3 (5 + 2 \sqrt{x})}{(5 - 2 \sqrt{x}) (5 + 2 \sqrt{x})}$

Step 4

Expand the denominator using the FOIL method.

$- \frac{3 (5 + 2 \sqrt{x})}{25 + 10 \sqrt{x} - 10 \sqrt{x} - 4 {\sqrt{x}}^{2}}$

Step 5

Simplify.

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Step 5.1

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

$- \frac{3 (5 + 2 \sqrt{x})}{25 - 4 {(x^{\frac{1}{2}})}^{2}}$

Step 5.2

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

$- \frac{3 (5 + 2 \sqrt{x})}{25 - 4 x^{\frac{1}{2} \cdot 2}}$

Step 5.3

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

$- \frac{3 (5 + 2 \sqrt{x})}{25 - 4 x^{\frac{2}{2}}}$

Step 5.4

Cancel the common factor of $2$ .

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Step 5.4.1

Cancel the common factor.

$- \frac{3 (5 + 2 \sqrt{x})}{25 - 4 x^{\frac{2}{2}}}$

Step 5.4.2

Rewrite the expression.

$- \frac{3 (5 + 2 \sqrt{x})}{25 - 4 x^{1}}$

Step 5.5

Simplify.

$- \frac{3 (5 + 2 \sqrt{x})}{25 - 4 x}$