An algebra problem by Dipa Parameswara

Algebra Level 4

Let $$f$$ be a functional equation that satisfy $$f(-x) - x f \left( \frac1x\right) = -\frac2x$$ for $$x\ne0$$.

If $$f(2017) = \frac mn$$, where $$m$$ and $$n$$ are coprime positive integers, find $$m+n$$.

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