Cubic summation

Algebra Level 4

\[\large \sum_{n=0}^{123456789} \dfrac{3n^2+9n+7}{(n^2+3n+2)^3} \]

Given that the summation above is equal to \(\dfrac AB\), where \(A\) and \(B\) are coprime positive integers, find \(B-A\).

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