"Spoooooooky" Russian rational expressions 11

Algebra Level 2

E=1(2a22a+2)(a3a+24) \mathscr{E} = 1- \left( \dfrac{2}{a-2} - \dfrac{2}{a+2} \right) \left( a-\dfrac{3a+2}{4} \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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