Question

Simplify the rational expression$\frac{y^2+3y-4}{y^2-6y+5}$

Short answer

Simplified form of s rational expression$\frac{y^2+3y-4}{y^2-6y+5}is\frac{(y+4)}{(y-5)},y\ne 5.$

Step-by-step solution

Step 1. Given expression

Given rational expression is $\frac{y^2+3y-4}{y^2-6y+5}$.

We have to simplify the given rational expression.

Step 2.  Simplification of the rational expression

To simplify the given rational expression ,first factor numerator and denominators separately and then divide out the common factor.

Then the simplified form of expression is $$\begin{gathered} \frac{y^2+3y-4}{y^2-6y+5}=\frac{(y+4)(y-1)}{(y-5)(y-1)} \\ =\frac{(y-4)}{(y-5)};y\ne 5\sin ce(y-1)isthecommonfactor. \end{gathered}$$