"Spoooooooky" Russian rational expressions 10

Algebra Level 2

E=(a2+2a+1)(1a+1+1a211a1) \mathscr{E} = (a^2 + 2a + 1) \left( \dfrac{1}{a+1} + \dfrac{1}{a^2 -1} - \dfrac{1}{a-1}\right)

Let a=2016 a = 2016 . If E \mathscr{E} can be expressed in the form xy - \dfrac{x}{y} , where xx and yy are coprime positive integers, find x+yx+y.


Credit: My former Trig teacher's worksheet of Russian rational expressions
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