Question

Find the domain of the rational function.

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

Short answer

The domain of the function is all real numbers. i.e.,$\left(-\infty ,\infty \right)$

Step-by-step solution

Step 1. Given information 

The given function is$H\left(x\right)=\frac{3x^2+x}{x^2+4}$

Step 2. Find the domain 

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

so,

$$\begin{gathered} x^2+4\ne 0 \\ {x}^2\ne -4 \end{gathered}$$

There is no solution of this equation.

So, The domain of the function is all real numbers. i.e.,$\left(-\infty ,\infty \right)$