Question 38065
The first step is to multiply everything by the lowest common denominator, which in this problem is (x^2 - 2x) or x(x - 2)...so from
x / (x-2) - (x+1) / x = 8 / (x^2 - 2x)
let's do just that...
(x(x - 2))[x / (x - 2) - (x + 1) / x = 8 / (x^2 - 2x)]
now cancel where you can and get
x^2 - (x + 1)(x - 2) = 8
Now expand, collect terms and solve
x^2 - x^2 + x + 2 = 8
x + 2 = 8
x = 6