Which one should I apply?

Algebra Level 3

\[ \large \dfrac{1}{c^2+a+b}+\dfrac{1}{b^2+a+c}+\dfrac{1}{a^2+b+c} \; . \]

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

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