Question

In the following exercises, find the domain of each function.

$R\left(x\right)=\frac{x^3-2x^2-25x+50}{x^2-25}$

Short answer

The domain is$R-\left\{-5,5\right\}$

Step-by-step solution

Given information

$R\left(x\right)=\frac{x^3-2x^2-25x+50}{x^2-25}$

We have to find the domain of the given rational function.

Factor the denominator

Set denominator zero

$$\begin{gathered} x^2-25=0 \\ \left(x-5\right)\left(x+5\right)=0 \end{gathered}$$

Use the Zero Product Property

$$\begin{gathered} \left(x-5\right)=0or\left(x+5\right)=0 \\ x=5,-5 \end{gathered}$$