Question

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

$R\left(x\right)=\frac{3x^2+15x}{6x^2+6x-36}$

Short answer

The domain is$R-\left\{-3,2\right\}$

Step-by-step solution

Given Information

$R\left(x\right)=\frac{3x^2+15x}{6x^2+6x-36}$

Step 2. Factor the denominator  

Set the denominator zero

$$\begin{gathered} 6x^2+6x-36=0 \\ 6\left(x^2+x-6\right)=0 \end{gathered}$$

$$\begin{gathered} 6\left(x^2+x-6\right)=0 \\ 6\left(x+3\right)\left(x-2\right)=0 \end{gathered}$$

Step 3. Use the Zero Product Property 

$$\begin{gathered} \left(x+3\right)=0or\left(x-2\right)=0 \\ x=-3,2 \end{gathered}$$