#### Answer

$\dfrac{x^{2}-x-72}{x^{2}-x-30}\div\dfrac{x^{2}+6x-27}{x^{2}-9x+18}=\dfrac{(x-9)(x+8)}{(x+5)(x+9)}$

#### Work Step by Step

$\dfrac{x^{2}-x-72}{x^{2}-x-30}\div\dfrac{x^{2}+6x-27}{x^{2}-9x+18}$
Factor both rational expressions completely:
$\dfrac{(x-9)(x+8)}{(x-6)(x+5)}\div\dfrac{(x+9)(x-3)}{(x-6)(x-3)}=...$
Evaluate the division and simplify by removing the factors that appear both in the numerator and the denominator:
$...=\dfrac{(x-9)(x+8)(x-6)(x-3)}{(x-6)(x+5)(x+9)(x-3)}=\dfrac{(x-9)(x+8)}{(x+5)(x+9)}$