"Spoooooooky" Russian rational expressions 8

Algebra Level 2

\[ \mathscr{E} = \dfrac{1-2x}{2x+1} + \dfrac{x^2 + 3x}{4x^2 -1} \div \dfrac{3+x}{4x+2} \]

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

You may use a calculator for the last step.


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