DE-BUNDESWETTBEWERB 2006 Problem 6

Find all functions $f: Q^{+}\rightarrow R$ such that

$f(x)+f(y)+2xyf(xy)=\frac{f(xy)}{f(x+y)}$ for all $x,y\in Q^{+}$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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