Answer
$-\frac{x+3}{x+2}$
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:
$\frac{x^{2}-x-12}{-x^{2}+2x+8}$
=$\frac{x^{2}+3x-4x-12}{-x^{2}-2x+4x+8}$
=$\frac{x(x+3)-4(x+3)}{-x(x+2)+4(x+2)}$
=$\frac{(x+3)(x-4)}{(x+2)(-x+4)}$
=$\frac{(x+3)(x-4)}{(-x+4)(x+2)}$
=$\frac{(x+3)(x-4)}{-(x-4)(x+2)}$
=$\frac{x+3}{-(x+2)}$
=$-\frac{x+3}{x+2}$
