# Trigonometry Related

Geometry Level 5

$\dfrac{2}{a^2 + 1} - \dfrac{2}{b^2 + 1} + \dfrac{3}{c^2 + 1}$

Given that $$a,b$$ and $$c$$ are positive real numbers satisfying $$abc + a + c = b$$. If the maximum value of the expression above can be expressed as $$\dfrac AB$$ for coprime positive integers $$A$$ and $$B$$, find the value of $$A+B$$.

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