"Spoooooooky" Russian rational expressions 1

Algebra Level 2

E=(20162017212016)÷(12017+12016) \mathscr{E} = \left( \dfrac{2016}{2017^2} - \dfrac{1}{2016} \right) \div \left( \dfrac{1}{2017} + \dfrac{1}{2016} \right)

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


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