Question

In the following exercises, simplify.

$\frac{a^2-a-12}{a^2-8a+16}$

Short answer

The result is$\frac{a+3}{a-4}$.

Step-by-step solution

Step 1. Given information.

Consider the given rational expression.

$\frac{a^2-a-12}{a^2-8a+16}$

Step 2. Calculation.

Factor the numerator and denominator and remove the common factor from the numerator and the denominator.

$\begin{array}{l}\frac{a^2-a-12}{a^2-8a+16}=\frac{a^2-4a+3a-12}{a^2-4a-4a+16}\\ =\frac{a\left(a-4\right)+3\left(a-4\right)}{a\left(a-4\right)-4\left(a-4\right)}\\ =\frac{\left(a-4\right)\left(a+3\right)}{\left(a-4\right)\left(a-4\right)}\\ =\frac{a+3}{a-4}\end{array}$