#### Answer

$\dfrac{9x+18}{4x^{2}-3x}\cdot\dfrac{4x^{2}-11x+6}{x^{2}-4}=\dfrac{9}{x}$

#### Work Step by Step

$\dfrac{9x+18}{4x^{2}-3x}\cdot\dfrac{4x^{2}-11x+6}{x^{2}-4}$
Factor both rational expressions completely:
$\dfrac{9x+18}{4x^{2}-3x}\cdot\dfrac{4x^{2}-11x+6}{x^{2}-4}=\dfrac{9(x+2)}{x(4x-3)}\cdot\dfrac{(4x-3)(x-2)}{(x+2)(x-2)}=...$
Evaluate the product of the two rational expressions and simplify by removing the factors that appear both in the numerator and the denominator of the resulting expression:
$...=\dfrac{9(x+2)(4x-3)(x-2)}{x(4x-3)(x+2)(x-2)}=\dfrac{9}{x}$