Question 85666
You need an LCD. Put the {{{x^2 - 2x}}} in factored form:

{{{x/(x - 2)}}} - {{{(x + 1)/x}}} = {{{8/(x(x - 2))}}}

Now it's easy to see that your LCD is x(x - 2). Multiply everything by x(x - 2):

(x)(x - 2)({{{x/(x - 2)}}} - {{{(x + 1)/x}}} = {{{8/(x(x - 2))}}})

Now the denominators cancel out and you have no more fractions:

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

{{{x^2}}} - {{{(x^2 - x - 2)}}} = 8
x + 2 = 8
x = 6
Check for extraneous solutions:

x = 6 isn't = 0
x - 2 = 6 = 2 = 4 isn't = 0
x = 6 is a good solution