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:

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"):

(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

Re: Reorganization of an inequality

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