"Spoooooooky" Russian rational expressions 7

Algebra Level pending

\[ \mathscr{E} = \left(\dfrac{p}{2q-p} \right) \left( \dfrac{4p-8}{p^3 - 2p^2} - \dfrac{q+2}{q^3 + 2q^2}\right) \]

Let \( p = 2016 \) and \( q = 2017 \). If \( \mathscr{E} \) can be expressed 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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