Answer
$\dfrac{x^{2}-2x-15}{x^{2}-6x+5}\div\dfrac{x^{2}-x-12}{x^{2}-1}=\dfrac{x+1}{x-4}$
Work Step by Step
$\dfrac{x^{2}-2x-15}{x^{2}-6x+5}\div\dfrac{x^{2}-x-12}{x^{2}-1}$
Factor both rational expressions completely:
$\dfrac{x^{2}-2x-15}{x^{2}-6x+5}\div\dfrac{x^{2}-x-12}{x^{2}-1}=...$
$...=\dfrac{(x-5)(x+3)}{(x-5)(x-1)}\div\dfrac{(x-4)(x+3)}{(x-1)(x+1)}=...$
Evaluate the division of the two fractions and simplify by removing the factors that appear both in the numerator and in the denominator of the resulting rational expression:
$...=\dfrac{(x-5)(x+3)(x-1)(x+1)}{(x-5)(x-1)(x-4)(x+3)}=...$
$...=\dfrac{x+1}{x-4}$
