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Part of 1991 Dutch Mathematical Olympiad

Problems(1)

easy inequality

Source: Netherlands 1991

Prove that for any three positive real numbers a,b,c, \frac{1}{a\plus{}b}\plus{}\frac{1}{b\plus{}c}\plus{}\frac{1}{c\plus{}a} \ge \frac{9}{2} \cdot \frac{1}{a\plus{}b\plus{}c}.

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