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Thread: Solve the complex fraction

  1. #1
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    Solve the complex fraction

    6 (x2y2)
    x−2y−2
    =?

    I was thinking along the lines of -6(x2-y2)/ 1/x2-y2 -> -6(x2-y2) *x2-y2 -> -6(x2-y2)2 but that's wrong
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  2. #2
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    Re: Solve the complex fraction

    Are you just trying to simplify the fraction rather than solve it?

    Also is your equation supposed to be this?
    $\displaystyle \frac{6(x^2-y^2)}{x^{-2}-y^{-2}}$

    From your attempt it appears that you are assuming $\displaystyle x^{-2}-y^{-2} = \frac{1}{x^2-y^2}$ but this is incorrect

    Instead this should be
    $\displaystyle x^{-2}-y^{-2} = \frac{1}{x^2}-\frac{1}{y^2}$
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  3. #3
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    Re: Solve the complex fraction

    I believe you mean simplify, rather than solve ...

    Denominator ...

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

    Now, numerator divided by denominator ...

    $\displaystyle 6(x^2-y^2) \div \frac{y^2-x^2}{x^2y^2} = ?$

    Finish it ...
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  4. #4
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    Re: Solve the complex fraction

    You're kinda close; hint:
    Denominator = 1/x^2 - 1/y^2 = -(x^2 - y^2) / (x^2 y^2)
    Notice that x^2-y^2 will cancel out...

    Leaving you the satisfaction of wrapping it up
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