Simplify (x^2)/(5+ square root of x^2+25)

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

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

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

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

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

Expand the denominator using the FOIL method.

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

Simplify.

Subtract $25$ from $25$ .

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

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

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

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

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

Apply the distributive property.

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

Multiply $- 1$ by $5$ .

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

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

Multiply $- 1$ by $- 1$ .

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

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

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