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

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.