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

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

Step 1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2

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

Factor $4$ out of $4 x$ .

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

Factor $4$ out of $- 16$ .

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

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

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

Step 3

Simplify the denominator.

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

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

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 $b = 4$ .

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

Step 4

Simplify terms.

Cancel the common factor of $x + 4$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x - 4$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Move $4$ to the left of $x + 4$ .

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