Algebra Examples

$\frac{x^{2}}{5 + \sqrt{x^{2} + 25}}$

Step 1

Multiply $\frac{x^{2}}{5 + \sqrt{x^{2} + 25}}$ by $\frac{5 - \sqrt{x^{2} + 25}}{5 - \sqrt{x^{2} + 25}}$ .

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

Step 2

Multiply $\frac{x^{2}}{5 + \sqrt{x^{2} + 25}}$ by $\frac{5 - \sqrt{x^{2} + 25}}{5 - \sqrt{x^{2} + 25}}$ .

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

Step 3

Expand the denominator using the FOIL method.

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

Step 4

Simplify.

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Step 4.1

Subtract $25$ from $25$ .

$\frac{x^{2} (5 - \sqrt{x^{2} + 25})}{- x^{2} + 0}$

Step 4.2

Add $- x^{2}$ and $0$ .

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

Step 5

Cancel the common factor of $x^{2}$ .

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Step 5.1

Cancel the common factor.

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

Step 5.2

Rewrite the expression.

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

Step 5.3

Move the negative one from the denominator of $\frac{5 - \sqrt{x^{2} + 25}}{- 1}$ .

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

Step 6

Rewrite $- 1 \cdot (5 - \sqrt{x^{2} + 25})$ as $- (5 - \sqrt{x^{2} + 25})$ .

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

Step 7

Apply the distributive property.

$- 1 \cdot 5 - - \sqrt{x^{2} + 25}$

Step 8

Multiply $- 1$ by $5$ .

$- 5 - - \sqrt{x^{2} + 25}$

Step 9

Multiply $- - \sqrt{x^{2} + 25}$ .

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Step 9.1

Multiply $- 1$ by $- 1$ .

$- 5 + 1 \sqrt{x^{2} + 25}$

Step 9.2

Multiply $\sqrt{x^{2} + 25}$ by $1$ .

$- 5 + \sqrt{x^{2} + 25}$