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Math Help - Factoring problem

  1. #1
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    Factoring problem

    How would i begin factoring this expression:

    (x^-2)-(y^-2)/(x^-1)-(y^-1)

    (reads x to the negative 2 minus y to the negative 2...)

    I just need somewhere to start...
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  2. #2
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    Quote Originally Posted by nascar77 View Post
    How would i begin factoring this expression:

    (x^-2)-(y^-2)/(x^-1)-(y^-1)

    (reads x to the negative 2 minus y to the negative 2...)

    I just need somewhere to start...
    Try writing them with positive powers first...

    \frac{x^{-2}-y^{-2}}{x^{-1} - y^{-1}} = \frac{\frac{1}{x^2} - \frac{1}{y^2}}{\frac{1}{x} - \frac{1}{y}}

     = \frac{\frac{y^2 - x^2}{x^2y^2}}{\frac{y - x}{xy}}

     = \frac{xy(y^2 - x^2)}{x^2y^2(y - x)}

     = \frac{y^2 - x^2}{xy(y - x)}

     = \frac{(y - x)(y + x)}{xy(y - x)}

     = \frac{y + x}{xy}.
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  3. #3
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    Quote Originally Posted by nascar77 View Post
    How would i begin factoring this expression:

    (x^-2)-(y^-2)/(x^-1)-(y^-1)

    (reads x to the negative 2 minus y to the negative 2...)

    I just need somewhere to start...
    The first thing I would do is multiply both numerator and denominator by x^2y^2:
    \frac{(x^{-2}-y^{-2})(x^2y^2)}{(x^{-1}- y^{-1})(x^2y^2)}= \frac{y^2- x^2}{xy^2- x^2y}
    You should be able to factor y^2- x^2 easily and xy^2- x^2y= xy(y- x).
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