Question

Solve $\frac{\left|x-2\right|}{x-2}>0$

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ \frac{\left|x-2\right|}{x-2}>0 \\ \mathrm{As},\left|x-2\right|=\left\{\begin{array}{l}x-2,x\ge 2\\ 2-x,x<2\end{array}\right. \\ \mathrm{And}\frac{\left|x-2\right|}{x-2}>0\mathrm{for}x>2 \\ \mathrm{So},x>2 \\ \therefore x\in \left(2,\infty \right) \end{gathered}$$