"Spoooooooky" Russian rational expressions 17

Algebra Level 4

\[ \mathscr{E} = \left( \dfrac{a-1}{3a + (a-1)^2} - \dfrac{1 - 3a + a^2}{a^3 - 1} - \dfrac{1}{a-1} \right) \div \dfrac{a^2 + 1}{1-a} \]

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


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