Answer
$4x-8$
Work Step by Step
Dividing with $\displaystyle \frac{P}{Q}$ equals multiplying with the reciprocal, $\displaystyle \frac{Q}{P}.$
$ \displaystyle \frac{x^{2}-4}{x-2}\div\frac{x+2}{4x-8}=\frac{x^{2}-4}{x-2}\cdot\frac{4x-8}{x+2}\qquad$... factor what you can
$=\displaystyle \frac{(x-2)(x+2)}{x-2}\cdot\frac{4(x-2)}{x+2}\qquad$... divide out the common factors
$=\displaystyle \frac{(1)(1)}{1}\cdot\frac{4(x-2)}{1}\qquad$
$=4(x-2)$
= $4x-8$
