Question

In the following exercises, simplify.

$\frac{y^2-2y-3}{y^2-9}$

Short answer

The result is$\frac{y+1}{y+3}$.

Step-by-step solution

Step 1. Given information.

Consider the given rational expression.

$\frac{y^2-2y-3}{y^2-9}$

Step 2. Calculation.

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

$\begin{array}{l}\frac{y^2-2y-3}{y^2-9}=\frac{y^2-3y+y-3}{y^2-3^2}\\ =\frac{y\left(y-3\right)+\left(y-3\right)}{\left(y+3\right)\left(y-3\right)}\\ =\frac{\left(y+1\right)\left(y-3\right)}{\left(y+3\right)\left(y-3\right)}\\ =\frac{y+1}{y+3}\end{array}$