Question

In the following exercises, simplify.

$\frac{y^2+3y-4}{y^2-6y+5}$

Short answer

The result is$\frac{y+4}{y-5}$.

Step-by-step solution

Step 1. Given information.

Consider the given rational expression.

$\frac{y^2+3y-4}{y^2-6y+5}$

Step 2. Calculation.

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

$\begin{array}{l}\frac{y^2+3y-4}{y^2-6y+5}=\frac{y^2+4y-y-4}{y^2-5y-y+5}\\ =\frac{y\left(y+4\right)-1\left(y+4\right)}{y\left(y-5\right)-1\left(y-5\right)}\\ =\frac{\left(y+4\right)\left(y-1\right)}{\left(y-5\right)\left(y-1\right)}\\ =\frac{y+4}{y-5}\end{array}$