How do I express "x" from this equation?: $y=x/(x^2+1)$

Question

How do I express "x" from this equation?: $y=x/(x^2+1)$. I am not able to express it.. What I really want to do is to find out values of this function: $f(x)=x/(x^2+1)$ if the domain is R{1,-1}. I have wanted to express "x" and than to solve inequations: $x<-1<x<1<x$ and the values of the function than would be the intersection of the results of those inequations (which is quite a long way to solve it, so if you know anything better..).