Can we divide two terms in finding solution for Linear Inequalities?

Solve the following inequality.

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

If x is greater than or equal to 2, it becomes: $\frac{x-2}{x-2}>0$, which can become $1>0$, which is true for all $x>2$ for when $x=2$,its value will become undefined. Is my solution correct?

Solve the following inequality.

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

If x is greater than or equal to 2, it becomes: $\frac{x-2}{x-2}>0$, which can become $1>0$, which is true for all $x>2$ for when $x=2$,its value will become undefined. Is my solution correct?