Simplify ((4x-8)/(x^2-4))÷(4/(-2x-4))

$\frac{4 x - 8}{x^{2} - 4} \div \frac{4}{- 2 x - 4}$

Step 1

To divide by a fraction, multiply by its reciprocal.

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

Step 2

Factor $4$ out of $4 x - 8$ .

Factor $4$ out of $4 x$ .

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

Factor $4$ out of $- 8$ .

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

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

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

Step 3

Simplify the denominator.

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

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

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 $b = 2$ .

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

Step 4

Simplify terms.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x - 2$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{x + 2} (- 2 x - 4)$

Multiply $\frac{1}{x + 2}$ by $- 2 x - 4$ .

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

Factor $2$ out of $- 2 x - 4$ .

Factor $2$ out of $- 2 x$ .

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

Factor $2$ out of $- 4$ .

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

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

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

Cancel the common factor of $- x - 2$ and $x + 2$ .

Factor $- 1$ out of $- x$ .

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

Rewrite $- 2$ as $- 1 (2)$ .

$\frac{2 (- (x) - 1 (2))}{x + 2}$

Factor $- 1$ out of $- (x) - 1 (2)$ .

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

Rewrite $- (x + 2)$ as $- 1 (x + 2)$ .

$\frac{2 (- 1 (x + 2))}{x + 2}$

Cancel the common factor.

$\frac{2 (- 1 (x + 2))}{x + 2}$

Divide $2 \cdot (- 1)$ by $1$ .

$2 \cdot (- 1)$

Multiply $2$ by $- 1$ .

$- 2$

Simplify ((4x-8)/(x^2-4))÷(4/(-2x-4))

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