"Spoooooooky" Russian rational expressions 1

Algebra Level 2

\[ \mathscr{E} = \left( \dfrac{2016}{2017^2} - \dfrac{1}{2016} \right) \div \left( \dfrac{1}{2017} + \dfrac{1}{2016} \right)\]

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


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