Answer
True
Work Step by Step
Using the rules of factoring trinomials to factorize the quadratic equations in both the numerator and the denominator:
$\frac{-2x^{2}-11x-12}{-3x^{2}-11x+4}$
=$\frac{-(2x^{2}+11x+12)}{-(3x^{2}+11x-4)}$
=$\frac{-(2x^{2}+3x+8x+12)}{-(3x^{2}-1x+12x-4)}$
=$\frac{-(x(2x+3)+4(2x+3))}{-(x(3x-1)+4(3x-1))}$
=$\frac{-(2x+3)(x+4)}{-(3x-1)(x+4)}$
Now, we cancel out the common factors in the numerator and denominator to simplify:
$\frac{-(2x+3)(x+4)}{-(3x-1)(x+4)}$
=$\frac{-(2x+3)}{-(3x-1)}$
=$\frac{(2x+3)}{(3x-1)}$
Therefore, the statement in the question is true.
