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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