CGMO 2004 Problem 2

Let $a, b, c$ be positive reals. Find the smallest value of $\frac {a + 3c}{a + 2b + c} + \frac {4b}{a + b + 2c} - \frac {8c}{a + b + 3c}.$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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