Answer
$\dfrac{36n^{2}-64}{3n^{2}-10n+8}\div\dfrac{3n^{2}-5n-12}{n^{2}-9n+14}=\dfrac{4(n-7)}{n-3}$
Work Step by Step
$\dfrac{36n^{2}-64}{3n^{2}-10n+8}\div\dfrac{3n^{2}-5n-12}{n^{2}-9n+14}$
Factor both rational expressions completely:
$\dfrac{4(9n^{2}-16)}{(3n-4)(n-2)}\div\dfrac{(3n+4)(n-3)}{(n-2)(n-7)}=...$
$...=\dfrac{4(3n-4)(3n+4)}{(3n-4)(n-2)}\div\dfrac{(3n+4)(n-3)}{(n-2)(n-7)}=...$
Evaluate the division of the two rational expressions and simplify by removing the factors that appear both in the numerator and the denominator of the resulting expression:
$...=\dfrac{4(3n-4)(3n+4)(n-2)(n-7)}{(3n-4)(n-2)(3n+4)(n-3)}=\dfrac{4(n-7)}{n-3}$
