Series Demystified-1

Algebra Level 4

n=150n2+3n+1n2+3n+2\sum_{n=1}^{50} \frac{n^2+3n+1}{n^2+3n+2} If the above series can be expressed as AB\frac A B, where AA & BB both are coprime positive integers, then find A+BA+B.

This is one of my original Series Demystified problems.
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