Answer
$\frac{x-6}{x+4}$
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:
$\frac{8x^{2}-51x+18}{8x^{2}+29x-12}$
=$\frac{8x^{2}-3x-48x+18}{8x^{2}-3x+32x-12}$
=$\frac{x(8x-3)-6(8x-3)}{x(8x-3)+4(8x-3)}$
=$\frac{(8x-3)(x-6)}{(8x-3)(x+4)}$
=$\frac{x-6}{x+4}$
