I get the LCM as X(X-2). If I apply LCM to right side of equation to each term to cancel out the fraction, I get

x(x-2) (1/x-2) - 2/x(x-2) . x(x-2) = 1

cancelling x(x-2) x-2=1 x=3. Also, could I have made this quadratic equation set to zero and solved for X, in which case x=2 or x=1.

I am a bit confused on the LCM. I get x(x-2) and you appear to get just (x-2), please explain. Also could solving and setting equation to zero also have worked???