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x+1/x-1 - 2/x^2-x=0
(x + 1) / (x - 1) - 2 / (x^2 - x) = 0.
Common denominator = (X^2 - x).
(x^2 + x - 2) / (x^2 - x),
Factor numerator and denominator:
(x - 1) (x + 2) / x(x - 1),
Cancel the (x - 1) factors and get:
(x + 2) / x = 0,
Cross multiply:
x + 2 = 0,
x = -2.
Check:
(-2 + 1) / (-2 -1) - 2 / ((-2)^2 - (-2)),
(-1 / -3) - 2 / 6,
1 / 3 - 1 / 3 = 0.