Cool Inequality #9 - 2 days to 2016, complex one

Algebra Level 5

\[ \large{\frac{a}{b+c}+\frac{b}{c+a}}\]

If \(a,b,c \) are positive reals with \(a \ge b \ge c\) and \( \dfrac{2b}{b+c} +\dfrac{a}{c} + \dfrac{2c}{a+c} =17 \). Find the maximum value of the expression above.

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