Question

Find the domain of the rational function.

$R\left(x\right)=\frac{5x^2}{3+x}$

Short answer

The domain of the given function is$\left(-\infty ,-3\right)\cup \left(-3,\infty \right)$

Step-by-step solution

Step 1.  Given information 

The given function is $R\left(x\right)=\frac{5x^2}{3+x}$

Step 2. Find the domain 

For the domain, the denominator should not be equal to zero.

So,

$$\begin{gathered} 3+x\ne 0 \\ x\ne -3 \end{gathered}$$

Thus, the domain of the given function is all real numbers except $-3$.

Therefore the domain is$\left(-\infty ,-3\right)\cup \left(-3,\infty \right)$