"Spoooooooky" Russian rational expressions 8

Algebra Level 2

E=12x2x+1+x2+3x4x21÷3+x4x+2 \mathscr{E} = \dfrac{1-2x}{2x+1} + \dfrac{x^2 + 3x}{4x^2 -1} \div \dfrac{3+x}{4x+2}

Let x=2016 x = 2016 . If E \mathscr{E} can be represented in the form ab \dfrac{a}{b} , where aa and bb are coprime positive integers, find a+ba+b.

You may use a calculator for the last step.

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

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