Simplify 8/(2x+8)*(x^2-16)/4

$\frac{8}{2 x + 8} \cdot \frac{x^{2} - 16}{4}$

Step 1

Factor $2$ out of $2 x + 8$ .

Factor $2$ out of $2 x$ .

$\frac{8}{2 (x) + 8} \cdot \frac{x^{2} - 16}{4}$

Factor $2$ out of $8$ .

$\frac{8}{2 x + 2 \cdot 4} \cdot \frac{x^{2} - 16}{4}$

Factor $2$ out of $2 x + 2 \cdot 4$ .

$\frac{8}{2 (x + 4)} \cdot \frac{x^{2} - 16}{4}$

Step 2

Simplify the numerator.

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

$\frac{8}{2 (x + 4)} \cdot \frac{x^{2} - 4^{2}}{4}$

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 $b = 4$ .

$\frac{8}{2 (x + 4)} \cdot \frac{(x + 4) (x - 4)}{4}$

Step 3

Reduce the expression by cancelling the common factors.

Cancel the common factor of $4$ .

Factor $4$ out of $8$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x + 4$ .

Factor $x + 4$ out of $2 (x + 4)$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{2}{2} \cdot (x - 4)$

Simplify the expression.

Divide $2$ by $2$ .

$1 \cdot (x - 4)$

Multiply $x - 4$ by $1$ .

$x - 4$