Cubic summation

Algebra Level 4

n=01234567893n2+9n+7(n2+3n+2)3\large \sum_{n=0}^{123456789} \dfrac{3n^2+9n+7}{(n^2+3n+2)^3}

Given that the summation above is equal to AB\dfrac AB, where AA and BB are coprime positive integers, find BAB-A.

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