An algebra problem by Karthik Kannan

Algebra Level 3

If the value of

r=1r3+(r2+1)2(r4+r2+1)(r2+r)\displaystyle\sum_{r=1}^{\infty} \frac{r^{3}+\left( r^{2}+1 \right)^{2}}{(r^{4}+r^{2}+1)(r^{2}+r)}

can be expressed as ab\displaystyle\frac{a}{b} where aa and bb are coprime positive integers, find the value of a+ba+b.

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