Question

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

Answer 1

We have,

$\frac{x^2}{x-2}>0\Rightarrow x-2\ge 0\left[\begin{array}{cc}\because \frac{a}{b}>0anda>0& \\ \Rightarrow b\ge 0& \end{array}\right]\Rightarrow x\ge 2\Rightarrow xϵ[2,\infty )\text{Hence,the solution set of the given inequation is}[2,\infty )$