Problem 12

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

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 $\large H+K+A$ .

This problem is in this Set .