Swapping in and out

Algebra Level 1

If \(f(x)=x+\frac{1}{x}\) and \(g(x)=x-\frac{1}{x}\), \(f \big( g(3) \big) = \frac{a}{b}\), where \(a\) and \(b\) are positive, coprime integers. What is \(a+b\)?

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