BALKAN-SL 2010 A1

Let $a,b$ and $c$ be positive real numbers. Prove that $\frac{a^2b(b-c)}{a+b}+\frac{b^2c(c-a)}{b+c}+\frac{c^2a(a-b)}{c+a} \ge 0.$

Dataset text AoPS wiki problems. Quoted with source.

Solutions

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