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Math Help - Please help

  1. #1
    zxe
    zxe is offline
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    Please help

    Express \frac{x+1}{x^2-x} - \frac{x-1}{x^2+x}as a fraction in its lowest terms.

    Im guessing the question means factorizing that equation,
    and i got this answer and i have no confident that it is right.
    \frac{4}{x^2-1}
    can anyone please help me?
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  2. #2
    Super Member wingless's Avatar
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    \frac{x+1}{x^2-x} - \frac{x-1}{x^2+x}

    \frac{x+1}{x(x-1)} - \frac{x-1}{x(x+1)}

    \left ( \frac{x+1}{x(x-1)}\cdot\frac{x+1}{x+1} \right ) - \left ( \frac{x-1}{x(x+1)}\cdot \frac{x-1}{x-1}\right )

    \frac{(x+1)^2}{x(x-1)(x+1)} - \frac{(x-1)^2}{x(x-1)(x+1)}

    \frac{(x+1)^2-(x-1)^2}{x(x-1)(x+1)}

    \frac{4\not x}{\not x(x-1)(x+1)}

    \frac{4}{(x-1)(x+1)}

    \frac{4}{x^2-1}

    You're right
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