Algebra Examples

$\frac{5}{5 + \sqrt{10 x}}$

Step 1

Multiply $\frac{5}{5 + \sqrt{10 x}}$ by $\frac{5 - \sqrt{10 x}}{5 - \sqrt{10 x}}$ .

$\frac{5}{5 + \sqrt{10 x}} \cdot \frac{5 - \sqrt{10 x}}{5 - \sqrt{10 x}}$

Step 2

Multiply $\frac{5}{5 + \sqrt{10 x}}$ by $\frac{5 - \sqrt{10 x}}{5 - \sqrt{10 x}}$ .

$\frac{5 (5 - \sqrt{10 x})}{(5 + \sqrt{10 x}) (5 - \sqrt{10 x})}$

Step 3

Expand the denominator using the FOIL method.

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

Step 4

Simplify.

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Step 4.1

Rewrite ${\sqrt{10 x}}^{2}$ as $10 x$ .

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Step 4.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{10 x}$ as ${(10 x)}^{\frac{1}{2}}$ .

$\frac{5 (5 - \sqrt{10 x})}{25 - {({(10 x)}^{\frac{1}{2}})}^{2}}$

Step 4.1.2

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

$\frac{5 (5 - \sqrt{10 x})}{25 - {(10 x)}^{\frac{1}{2} \cdot 2}}$

Step 4.1.3

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

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

Step 4.1.4

Cancel the common factor of $2$ .

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Step 4.1.4.1

Cancel the common factor.

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

Step 4.1.4.2

Rewrite the expression.

$\frac{5 (5 - \sqrt{10 x})}{25 - {(10 x)}^{1}}$

Step 4.1.5

Simplify.

$\frac{5 (5 - \sqrt{10 x})}{25 - (10 x)}$

Step 4.2

Multiply $10$ by $- 1$ .

$\frac{5 (5 - \sqrt{10 x})}{25 - 10 x}$

Step 5

Cancel the common factors.

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Step 5.1

Factor $5$ out of $25$ .

$\frac{5 (5 - \sqrt{10 x})}{5 (5) - 10 x}$

Step 5.2

Factor $5$ out of $- 10 x$ .

$\frac{5 (5 - \sqrt{10 x})}{5 (5) + 5 (- 2 x)}$

Step 5.3

Factor $5$ out of $5 (5) + 5 (- 2 x)$ .

$\frac{5 (5 - \sqrt{10 x})}{5 (5 - 2 x)}$

Step 5.4

Cancel the common factor.

$\frac{5 (5 - \sqrt{10 x})}{5 (5 - 2 x)}$

Step 5.5

Rewrite the expression.

$\frac{5 - \sqrt{10 x}}{5 - 2 x}$