Answer
True
Work Step by Step
Using the rules of factoring trinomials to factor the quadratic equations in both the numerator and the denominator, we obtain:
$\frac{x^{2}+5x-14}{x^{2}-8x+12}$
=$\frac{x^{2}-2x+7x-14}{x^{2}-2x-6x+12}$
=$\frac{x(x-2)+7(x-2)}{x(x-2)-6(x-2)}$
=$\frac{(x-2)(x+7)}{(x-2)(x-6)}$
Now, we cancel out the common factors in the numerator and denominator to simplify:
$\frac{(x-2)(x+7)}{(x-2)(x-6)}=\frac{x+7}{x-6}$
Therefore, the statement in the question is true.
