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Math Help - simplify fraction

  1. #1
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    simplify fraction

    Hey, this one's probably real simple, but I'm stuck.

    I'd like to see the work and answer for performing the operations and simplifying this:

    x-y - x+y
    x+y x-y
    x+y - x-y
    x-y x+y

    I'd appreciate any help. Like I said I'm sure it's easy, I'm just stuck.

    -Worthey1987
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  2. #2
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    Hello, Worthey1987!

    Could there be a typo in the problem? . . . It's too easy!


    Simplify: . \frac{\dfrac{x-y}{x+y} - \dfrac{x+y}{x-y}}{\dfrac{x+y}{x-y} - \dfrac{x-y}{x+y}}
    Factor -1 out of the numerator: . \frac{\text{-}1\bigg[\dfrac{x+y}{x-y} - \dfrac{x-y}{x+y}\bigg]}{\;\;\;\bigg[\dfrac{x+y}{x-y} - \dfrac{x-y}{x+y}\bigg]} . . . and reduce.

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  3. #3
    o_O
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    Just a little colour-coding: \frac{\ \displaystyle {\color{red}\frac{x-y}{x+y}} - {\color{blue}\frac{x-y}{x+y}} \ }{\ \displaystyle {\color{blue}\frac{x+y}{x-y}} - {\color{red}\frac{x-y}{x+y}} \ }

    Factor out a -1 from the numerator: = \frac{\ - \left( \displaystyle   {\color{blue}\frac{x-y}{x+y}} - {\color{red}\frac{x-y}{x+y}}\right) \ }{\ \displaystyle {\color{blue}\frac{x+y}{x-y}} - {\color{red}\frac{x-y}{x+y}} \ }

    Notice that the thing in parentheses is the same as the same as the bottom. What can you do to them?
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