Answer
$\frac{5x-2}{4x-3}$
Work Step by Step
Since the numerator and the denominator both consist of a trinomial, we use the rules of factoring trinomials in order to factor them. Then, we cancel out the resultant common factors in the numerator and the denominator:
$\frac{5x^{2}-32x+12}{4x^{2}-27x+18}$
=$\frac{5x^{2}-2x-30x+12}{4x^{2}-3x-24x+18}$
=$\frac{x(5x-2)-6(5x-2)}{x(4x-3)-6(4x-3)}$
=$\frac{(5x-2)(x-6)}{(4x-3)(x-6)}$
=$\frac{5x-2}{4x-3}$
