#### Answer

$\dfrac{8n^{2}-18}{2n^{2}-5n+3}\div\dfrac{6n^{2}+7n-3}{n^{2}-9n+8}=\dfrac{2(n-8)}{3n-1}$

#### Work Step by Step

$\dfrac{8n^{2}-18}{2n^{2}-5n+3}\div\dfrac{6n^{2}+7n-3}{n^{2}-9n+8}$
Factor both rational expressions completely:
$\dfrac{2(4n^{2}-9)}{(n-1)(2n-3)}\div\dfrac{(2n+3)(3n-1)}{(n-1)(n-8)}=...$
$...=\dfrac{2(2n-3)(2n+3)}{(n-1)(2n-3)}\div\dfrac{(2n+3)(3n-1)}{(n-1)(n-8)}=...$
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:
$...=\dfrac{2(2n-3)(2n+3)(n-1)(n-8)}{(n-1)(2n-3)(2n+3)(3n-1)}=\dfrac{2(n-8)}{3n-1}$