Answer
$\frac{(x+2)}{(5x+4)}$
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:
$\frac{-2x^{2}-x+6}{-10x^{2}+7x+12}$
=$\frac{-(2x^{2}+x-6)}{-(10x^{2}-7x-12)}$
=$\frac{-(2x^{2}-3x+4x-6)}{-(10x^{2}+8x-15x-12)}$
=$\frac{-(x(2x-3)+2(2x-3))}{-(2x(5x+4)-3(5x+4))}$
=$\frac{-(2x-3)(x+2)}{-(5x+4)(2x-3)}$
=$\frac{-(x+2)}{-(5x+4)}$
=$\frac{(x+2)}{(5x+4)}$
