Which one should I apply?

Algebra Level 3

1c2+a+b+1b2+a+c+1a2+b+c  . \large \dfrac{1}{c^2+a+b}+\dfrac{1}{b^2+a+c}+\dfrac{1}{a^2+b+c} \; .

If a,ba,b and cc are positive numbers satisfying a+b+c=3a+b+c=3, find maximum value of the expression above.

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