Let $F(x)$ be a real valued function defined for all real $x$ except for $x=0$ and $x=1$ and satisfying the functional equation $F(x)+F\{(x-1) / x\}=1+x$. Find all functions $F(x)$ satisfying these conditions. The original answer is in the format \frac{m}{n}, please provide the value of m + n when x = 2.

Let's think step by step and output the final answer within \boxed{}.
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