# Unbalanced Symmetric Inequality

Algebra Level 5

$\large \dfrac{ab}{c^2+3}+\dfrac{bc}{a^2+3}+\dfrac{ca}{b^2+3}$

Given that $$a,b$$ and $$c$$ are positive reals satisfying $$a+b+c=3$$. If the maximum value of the expression above can be expressed as $\dfrac{A\sqrt{B}-C}{D} \; ,$ where $$A,B,C$$ and $$D$$ are positive integers such that $$\gcd(A,C)=\gcd(A,D)=1$$ and $$B$$ is square-free, determine $$A+B+C+D$$.

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