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Thread: Factoring a complex equation

  1. #1
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    Question Factoring a complex equation

    Hi,

    Can someone help me figure out how to factor $\frac{e}{x^2} - e^3$ so that I get some factor, y, such that y(x - $\frac{1}{e}$) = $\frac{e}{x^2} - e^3$?

    I'm having quite a tough time figuring out what y should be
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  2. #2
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    Re: Factoring a complex equation

    well it's pretty clear that

    $y = \dfrac{\frac{e}{x^2}-e^3}{x-\frac 1 e},~\forall x \neq \dfrac 1 e$

    $y = \dfrac{\frac{e-x^2e^3}{x^2}}{\frac{xe-1}{e}}$

    $y = \dfrac{e^2(1-x^2 e^2)}{x^2(xe-1)}$

    This can be simplified a bit further

    $y = -\dfrac{e^2(1-xe)(1+xe)}{x^2(1-xe)} = -\dfrac{e^2(1+x e)}{x^2}$
    Thanks from topsquark
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