Question

Simplify the rational expression$\frac{y^2-2y-3}{y^2-9}.$

Short answer

Simplified form of the rational expression$\frac{y^2-2y-3}{y^2-9}is\frac{(y+1)}{(y+3)};y\ne -3.$

Step-by-step solution

. Given information

Given rational expression is$\frac{y^2-2y-3}{y^2-9}$ $\frac{y^2-2y-3}{y^2-9}$.

We have to simplify the given rational expression.

Step 2.  Simplification of the rational expression

To simplify we have find out the factors of both numerator and denominator separately and then divide out the common factor.

So the given rational expression becomes $$\begin{gathered} \frac{y^2-2y-3}{y^2-9}=\frac{(y-3)(y+1)}{(y-3)(y+3)} \\ =\frac{(y+1)}{(y+3)};y\ne -3here(y-3)isthecommonfactor. \end{gathered}$$