# Can we divide two terms in finding solution for Linear Inequalities? Solve the following inequality. (|x-2|)/(x-2)>0

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?
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Giancarlo Callahan
Just three cases:
$x>2$ gives $1>0$, which is true.
$x<2$ gives $-1>0$, which is wrong and
$x=2$, which is impossible.
After all these things we got the answer: $\left(2,+\mathrm{\infty }\right)$