"Spoooooooky" Russian rational expressions 17

Algebra Level 4

E=(a13a+(a1)213a+a2a311a1)÷a2+11a \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 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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