KöMaL 2007 A435

Prove $(a+b+c)\left(\frac1a+\frac1b+\frac1c\right) \ge 6\left(\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}\right)$ whenever 1 $\le a$ , $b$ , $c \le$ 2.

Official text KöMaL. Quoted with source.

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