Question

In the following exercises, simplify.

$\frac{x^2-25}{x^2+2x-15}$

Short answer

The result is$\frac{x-5}{x-3}$.

Step-by-step solution

Step 1. Given information.

Consider the given rational expression.

$\frac{x^2-25}{x^2+2x-15}$

Step 2. Calculation.

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

$\begin{array}{l}\frac{x^2-25}{x^2+2x-15}=\frac{x^2-5^2}{x^2+5x-3x-15}\\ =\frac{\left(x+5\right)\left(x-5\right)}{x\left(x+5\right)-3\left(x+5\right)}\\ =\frac{\left(x+5\right)\left(x-5\right)}{\left(x+5\right)\left(x-3\right)}\\ =\frac{x-5}{x-3}\end{array}$