First, there are two points where denominator = 0, x = 1 and x = -1. f(x) tends to infinity at these points (numerator not =0 at them). So there are two vertical asymptotes, x=1 and x=-1.

At +-infinity f(x) obviously tends to 0 (approx. as 1/x), so there is one horizontal asymptote, y=0.