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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