Can you sum this?

Algebra Level 4

S=32+1321+52+1521+72+1721++20152+1201521\large{S = \dfrac{3^2 + 1}{3^2 - 1} + \dfrac{5^2 + 1}{5^2 - 1} + \dfrac{7^2 + 1}{7^2 - 1} + \ldots + \dfrac{2015^2 + 1}{2015^2 - 1}}


If SS can be expressed as AB\dfrac{A}{B} for positive coprime integers A,BA,B, then find the value of A+BA+B.

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