Answer
$-\frac{x+9}{x+6}$
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:
$\frac{x^{2}+7x-18}{-x^{2}-4x+12}$
=$\frac{x^{2}-2x+9x-18}{-x^{2}+2x-6x+12}$
=$\frac{x(x-2)+9(x-2))}{-x(x-2)-6(x-2)}$
=$\frac{(x-2)(x+9)}{(x-2)(-x-6)}$
=$\frac{(x+9)}{-x-6}$
=$\frac{x+9}{-(x+6)}$
=$-\frac{x+9}{x+6}$
