Solution:

It is given that: |x – 2| / (x – 2) > 0

The above equation clearly states that x≠2 so two cases arise:

Case1: x–2>0

It implies that : x>2

In this case, we have:  |x–2| = x – 2

x ϵ (2, ∞)….(1)

Case 2:

x–2<0

This implies that x<2

In this case, |x–2|= – (x–2)

– (x – 2) / (x – 2) > 0

– 1 > 0

Inequality doesn’t satisfy in this case. So, this case gets nullified.

Therefore, x ∈ (2, ∞) from (1)