x/x-2 - x+1/x = 8/x^2-2x

Question

notice the last denominator factors to x(x-2) and those factors are found in the other two fractions
so x(x-2) is the lowest common denominator.

now multiply each term by that x(x-2) to get

(x)(x) -(x+1)(x-2) = 8

simplify and solve

I got x=6