# Write the solution of the inequation

Question:

Write the solution of the inequation $\frac{x^{2}}{x-2}>0$.

Solution:

We have,

$\frac{x^{2}}{x-2}>0$

Equating both the numerator and the denominator with zero, we obtain $x=0$ and $x=2$ as critical points.

Plotting these points on the real line, we see that the real line is divided into three regions.

Therefore, the solution set of the given inequality is $x \in(2, \infty)$.