Question

Find the domain of the rational function.

$R\left(x\right)=\frac{4x}{x-3}$

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$R\left(x\right)=\frac{4x}{x-3}$.

Step 2. Find the domain

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

So,

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

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

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