Simplify (x^3+8x^2)/(x^2-64)

$\frac{x^{3} + 8 x^{2}}{x^{2} - 64}$

Factor $x^{2}$ out of $x^{3} + 8 x^{2}$ .

Factor $x^{2}$ out of $x^{3}$ .

$\frac{x^{2} x + 8 x^{2}}{x^{2} - 64}$

Factor $x^{2}$ out of $8 x^{2}$ .

$\frac{x^{2} x + x^{2} \cdot 8}{x^{2} - 64}$

Factor $x^{2}$ out of $x^{2} x + x^{2} \cdot 8$ .

$\frac{x^{2} (x + 8)}{x^{2} - 64}$

Simplify the denominator.

Rewrite $64$ as $8^{2}$ .

$\frac{x^{2} (x + 8)}{x^{2} - 8^{2}}$

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 $b = 8$ .

$\frac{x^{2} (x + 8)}{(x + 8) (x - 8)}$

Cancel the common factor of $x + 8$ .

Cancel the common factor.

$\frac{x^{2} (x + 8)}{(x + 8) (x - 8)}$

Rewrite the expression.

$\frac{x^{2}}{x - 8}$