Question

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

$R\left(x\right)=\frac{x^3+3x^2-4x-12}{x^2-4}$

Short answer

The domain is$R-\left\{-2,2\right\}$

Step-by-step solution

Given Information

$R\left(x\right)=\frac{x^3+3x^2-4x-12}{x^2-4}$

Step 2. Factor the denominator 

Set denominator zero

$$\begin{gathered} x^2-4=0 \\ \left(x-2\right)\left(x+2\right)=0 \end{gathered}$$

Step 3. Use the Zero Product Property 

$$\begin{gathered} x-2=0orx+2=0 \\ x=2,-2 \end{gathered}$$