CWMO 2011 Problem 1

Given that $0 < x,y < 1$ , find the maximum value of $\frac{xy(1-x-y)}{(x+y)(1-x)(1-y)}$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.