Finding out intersections of x^2 / (1+x^2) and rx-s?

Question

Two equations:
x^2 / (1+x^2) and rx-s where r>0 and s>=0
Is there a way to find out in which cases they intersect 1,2, or 3 times in terms of r and s without dealing with a nasty cubic equation?

Answer 1

sorry there is none.

meaning... you have to do the nasty...

but I can give you this:
http://www.walterzorn.com/grapher/grapher_e.htm
at least you can plot the two curves and from then make an educated guess of the intersection, hopefully if the value is rational. d: