f(x)+g(x)=1/x-1……1
f(-x)+g(-x)=-1/x+1
-f(x)+g(x)=-1/x+1……2
1,2相减：
2f(x)=1/(x-1)+1/(x+1)=2x/(x+1)(x-1)
f(x)=x/[(x+1)(x-1)]