If m+1/(m-2)=4, then find the value of (m-2)^2+1/((m-2)^2).

If $m+\frac{1}{m-2}=4$

Subtract -2 on both the sides 

If $m - 2 +\frac{1}{m-2}=4 - 2$

If $m - 2 +\frac{1}{m-2}=2$

Then the value of $(m-2)^2+\frac{1}{(m-2)^2}$ = 2² - 2 = 2