# Trigonometry Related Part IV

Geometry Level 5

$\frac{1}{a^2+1}+\frac{4}{b^2+4}+\frac{9}{c^2+9}$

Given that $$a,b$$ and $$c$$ are positive real numbers satisfying $$3ab+bc+2ca=6$$.

If the maximum value of the expression above can be expressed as $$\frac{A}{B}$$ for coprime positive integers $$A$$ and $$B$$, determine $$A+B$$.

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