Recall the rule lnA - lnB =ln(A/B). Apply that to LHS.
Then you'll have ln [(x+1)/(x-2)} = ln x
Drop the lns so that (x+1)/(x-2)=x
This becomes x+1 = x(x-2) which gives a quadratic and go from there.
Remember to check your answers from the quadratic in the ORIGINAL log equation. Reject answers which don't give pos values for x+1, x-2 or x as ln A is not defined for non-positive A valus.