Simplify (4x^2+16x)/(x^2-16)

$\frac{4 x^{2} + 16 x}{x^{2} - 16}$

Step 1

Factor $4 x$ out of $4 x^{2} + 16 x$ .

Factor $4 x$ out of $4 x^{2}$ .

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

Factor $4 x$ out of $16 x$ .

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

Factor $4 x$ out of $4 x (x) + 4 x (4)$ .

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

Step 2

Simplify the denominator.

Rewrite $16$ as $4^{2}$ .

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

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 4$ .

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

Step 3

Cancel the common factor of $x + 4$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{4 x}{x - 4}$