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Math Help - Reorganization of an inequality

  1. #1
    pul
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    Reorganization of an inequality

    Hi everyone, the origin of the problem is not really "pre-university" but the math behind it should be trivial. Here we go:

    \frac{(n-1)x}{n}+y>\frac{(x+y)x}{2x+y}+\left(\frac{n-1}{n}\right)\frac{x^{3}}{(2x+y)^{2}}+\left(\frac{x  }{2x+y}\right)y

    I simply need to rearrange this for illustrative purposes (I'd like to show quickly for which n the above condition is met; it's from a paper on auction theory).

    Now Wolfram Alfra returns me a rather striking alternate form ("Alternate form assuming n, x and y are positive"):

    (n-3)x^2+(2n-1)y+ny^2>0

    (link: http://www.wolframalpha.com/input/?i=\frac{(n-1)x}{n}%2By>\frac{(x%2By)x}{2x%2By}%2B\left(\frac{ n-1}{n}\right)\frac{x^{3}}{(2x%2By)^{2}}%2B\left(\fr ac{x}{2x%2By}\right)\cdot+y)

    Does anyone have a clue how to get to that?

    Any help is appreciated.

    Cheers,
    Patrick
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  2. #2
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    Re: Reorganization of an inequality

    Take all the terms to the left and get a common denominator?
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