#### Answer

$\dfrac{x^{2}-5x-24}{x^{2}-x-12}\div\dfrac{x^{2}-10x+16}{x^{2}+x-6}=\dfrac{x+3}{x-4}$

#### Work Step by Step

$\dfrac{x^{2}-5x-24}{x^{2}-x-12}\div\dfrac{x^{2}-10x+16}{x^{2}+x-6}$
Factor both rational expressions completely:
$\dfrac{(x-8)(x+3)}{(x-4)(x+3)}\div\dfrac{(x-8)(x-2)}{(x+3)(x-2)}=...$
Evaluate the division and simplify by removing the factors that appear both in the numerator and the denominator of the resulting expression:
$...=\dfrac{(x-8)(x+3)^{2}(x-2)}{(x-4)(x+3)(x-8)(x-2)}=\dfrac{x+3}{x-4}$