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Math Help - Difficult fraction problem

  1. #1
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    Difficult fraction problem

    I don't know how this can be simplified or solved, tried synthetic division.. no good.
    Help appreciated

     \frac {x^4 +(2xy^2)^2 -3y}{(xy)^2}
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  2. #2
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    Re: Difficult fraction problem

    I don't know if you would consider this simpler, but

    \displaystyle \begin{align*} \frac{x^4 + (2xy^2)^2 - 3y}{(xy)^2} &= \frac{x^4 + 2x^2y^4 - 3y}{x^2y^2} \\ &= \frac{x^4}{x^2y^2} + \frac{2xy^2}{x^2y^2} - \frac{3y}{x^2y^2} \\ &= \frac{x^2}{y^2} + \frac{2}{x} - \frac{3}{x^2y} \end{align*}
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  3. #3
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    Re: Difficult fraction problem

    I've done that, but it seems incomplete.
    I feel like I'm missing something.
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  4. #4
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    Re: Difficult fraction problem

    Quote Originally Posted by Prove It View Post
    I don't know if you would consider this simpler, but

    \displaystyle \begin{align*} \frac{x^4 + (2xy^2)^2 - 3y}{(xy)^2} &= \frac{x^4 + 2x^2y^4 - 3y}{x^2y^2} \\ &= \frac{x^4}{x^2y^2} + \frac{2xy^2}{x^2y^2} - \frac{3y}{x^2y^2} \\ &= \frac{x^2}{y^2} + \frac{2}{x} - \frac{3}{x^2y} \end{align*}
    No, (2xy^2)^2= 4x^2y^4 so that should be
    \frac{x^4 + (2xy^2)^2 - 3y}{(xy)^2} &= \frac{x^4 + 4x^2y^4 - 3y}{x^2y^2}
    and the final result should be
     \frac{x^2}{y^2} + \frac{4}{x} - \frac{3}{x^2y}
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