"Spoooooooky" Russian rational expressions 10

Algebra Level 2

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

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