"Spoooooooky" Russian rational expressions 10

Algebra Level pending

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

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