Another Functional Equation Past Time

Algebra Level pending

Given that for \(x \in \mathbb{R} , x \neq 1, -1\),

\[f(\frac{x-3}{x+1}) + f(\frac{3+x}{1-x}) = x\],

\(f(2)\) can be expressed as \(-\frac{m}{n} \) where \(m, n\) are relatively prime. Find \(m+n\).

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