A Nice Inequality

Algebra Level 4

12a+b+12b+c+12c+a\large \dfrac{1}{2a+b}+\dfrac{1}{2b+c}+\dfrac{1}{2c+a} If a,ba,b and c c are positive reals satisfying 1a+1b+1c=1\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}=1, find the maximum value of the expression above.

Submit your answer to 3 decimal places

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