Question

If $\frac{1}{x-2}>0$, then $x$ lies in

• A. $(2,\infty )$
• B. $[2,\infty )$
• C. $(-2,\infty )-\left\{2\right\}$
• D. $[-2,\infty )-\left\{2\right\}$

Answer 1

The correct option is A $(2,\infty )$

$\frac{1}{x-2}>0$
$\Rightarrow x-2>0$ and $x\ne 2$
$\Rightarrow x>2$ and $x\ne 2$
$\Rightarrow x\in (2,\infty )$