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algebra

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Solve and check all proposed solutions.
Show work for solving and for checking.
x+1/x-1 - 2/x^2-x=0

  • algebra -

    (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.

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