Question

Simplify the rational expression$\frac{a^2-4}{a^2+6y-16}$

Short answer

Simplified form of the rational expression$\frac{a^2-16}{a^2+6y-16}is\frac{(a+2)}{(a+8)};a\ne -8.$

Step-by-step solution

. Given information

Given rational expression is $\frac{a^2-4}{a^2+6y-16}.$

We have to simplify the given expression.

. Simplification of the rational expression

To simplify the given rational expression find out factors of both numerator and numerator separately and divide out the common factor. So the simplified form of $$\begin{gathered} \frac{a^2-4}{a^2+6y-16}=\frac{(a+2)(a-2)}{(a-2)(a+8)} \\ =\frac{(a+2)}{(a+8)};a\ne -8\sin ce(a-2)isthecommonfacor. \end{gathered}$$