Question

Simplify the rational expression$\frac{20-5y}{y^2-16}$

Short answer

The simplified form of$\frac{20-5y}{y^2-16}is\frac{-5}{(y+4)},y\ne -4.$

Step-by-step solution

. Given information

Given rational expression is $\frac{20-5y}{y^2-16}$.

We have to simplify the given rational expression.

. Simplification of the rational expression

To simply first we need to factor both numerator and denominator separately and find out the common factor, then simplify,
$$\begin{gathered} \frac{20-5y}{y^2-16}=\frac{5(4-y)}{(y+4)(y-4)} \\ =\frac{-5(y-4)}{(y+4)(y-4)},anexpressionanditsoppositetodividesis-1 \\ =\frac{-5}{(y+4)};y\ne -4,commonfactordivideout. \\ Thisisthesimplifiedformofthegivenexpression. \end{gathered}$$