Question

Hello! It’s Rose I’m having trouble with this ACT practice problem, *Enter your answer by filling in the boxes. Enter your answer so that each rational expression is in simplified form.*

Answer 1

Here, the denominator of the given expression is a quadratic expression whose factors are (x+3) and (x-4). So, the given expression can be written as:

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

Now, separate the terms in the numerator as follows:

$\frac{2x-2}{(x+3)(x-4)}=\frac{2x}{(x+3)(x-4)}+\frac{-2}{(x+3)(x-4)}$

Therefore, the required answer is given below: