# Problem 12

Algebra Level 5

$\frac{4(a+c)}{a^2+3c^2+28}+\frac{4a}{a^2+bc+7}-\frac{5}{(a+b)^2}-\frac{3}{a(b+c)}$

Given that $$a,b,c$$ are positive reals and $$a^2+b^2+c^2=14$$.If the maximum value of the expression above can be expressed as $$\large \frac{H}{K}$$ and the sum of $$a,b,c$$ when the equality holds is $$\large A$$.

Compute $$\large H+K+A$$.

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