Answer
$1$
Work Step by Step
Dividing with $\displaystyle \frac{P}{Q}$ equals multiplying with the reciprocal, $\displaystyle \frac{Q}{P}.$
$\displaystyle \frac{x^{2}-4}{x^{2}+3x-10}\div\frac{x^{2}+5x+6}{x^{2}+8x+15}=\frac{x^{2}-4}{x^{2}+3x-10}\cdot\frac{x^{2}+8x+15}{x^{2}+5x+6}\qquad$... factor what you can
$x^{2}-4=(x+2)(x-2)$
$x^{2}+3x-10=(x+5)(x-2)$
$x^{2}+8x+15=(x+5)(x+3)$
$x^{2}+5x+6=(x+2)(x+3)$
$=\displaystyle \frac{(x+2)(x-2)}{(x+5)(x-2)}\cdot\frac{(x+5)(x+3)}{(x+2)(x+3)} \qquad$... divide out the common factors
$=\displaystyle \frac{(1)(1)}{(1)(1)}\cdot\frac{(1)(1)}{(1)(1)} $
= $1$
