Let $a, b$ and $c$ be real numbers such that $\frac{a}{b + c}+\frac{b}{c + a}+\frac{c}{a + b}= 1$. Prove that $\frac{a^2}{b + c}+\frac{b^2}{c + a}+\frac{c^2}{a + b}= 0$.
Source: 2005 Estonia National Olympiad Final Round grade 10 p2
Tags: algebra
Let $a, b$ and $c$ be real numbers such that $\frac{a}{b + c}+\frac{b}{c + a}+\frac{c}{a + b}= 1$. Prove that $\frac{a^2}{b + c}+\frac{b^2}{c + a}+\frac{c^2}{a + b}= 0$.