Answer
$\dfrac{2x^{2}-9x+9}{8x-12}\div\dfrac{x^{2}-3x}{2x}=\dfrac{1}{2}$
Work Step by Step
$\dfrac{2x^{2}-9x+9}{8x-12}\div\dfrac{x^{2}-3x}{2x}$
Factor both rational expressions completely:
$\dfrac{2x^{2}-9x+9}{8x-12}\div\dfrac{x^{2}-3x}{2x}=\dfrac{(2x-3)(x-3)}{4(2x-3)}\div\dfrac{x(x-3)}{2x}=...$
Evaluate the division and simplify by removing the factors that appear both in the numerator and the denominator of the resulting expression:
$...=\dfrac{2x(2x-3)(x-3)}{4x(2x-3)(x-3)}=\dfrac{1}{2}$