f(x) = (1+x) / (1 + x^2)

what are the inflection points?

I got f '(x) = - (x^2 + 2x -1) / (x^4 + 2x + 1)

I got f ''(x) = (2x^3 + 6x^2 - 6x - 2) / (x^6 + 3x^4 + 3x^2 + 1)

Now When I set f ''(x) = zero to find the inflection point(s), How can I solve for x....this is...amazingly hard.