Let \( f(x) = \frac{x - 1}{x + 2} \). Define \( g(x) \) as the inverse of \( f(x) \). If \( h(x) = f(g(x)) + g(f(x)) \), find the value of \( h(3) \). Let's think step by step and output the final answer within \boxed{}.
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