Solution: Because f (x)+g (x) =1(x-1) ... (1), f (-x)+g (-x) =1(-x-6544).

And f(x) is an even function, g(x) is odd function, f (x)-g (x) =-1/(x+1) ... (2),

(1)+(2) gives 2f (x) = 2/(x 2-1), so f (x) =1/(x 2-1), (1)