# How do you solve x/(x-3)>0?

Jan 17, 2017

$f \left(x\right) > 0$ for $\left(- \infty , 0\right] \cup \left[3 , + \infty\right)$

#### Explanation:

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

$\therefore f \left(x\right) \le 0$ for $0 \le x < 3$

Hence $f \left(x\right) > 0$ for $\left(- \infty , 0\right] \cup \left[3 , + \infty\right)$

NB: $f \left(x\right)$ is undefined at $x = 3$

This can be seen from the graph of $f \left(x\right)$ below.

graph{x/(x-3) [-16.02, 16.02, -8, 8.02]}