y=(2x)/(x^2-1) Graph the function.

We are asked to graph the function y=(2x)/(x^2-1) :
Factoring the denominator we get:
y=(2x)/((x+1)(x-1))
The graph has vertical asymptotes at x=1 and x=-1. The horizontal asymptote is y=0.
The y-intercept is 0 as is the only x-intercept.
The first derivative is y'=(-2(x^2+1))/((x^2-1)^2) so the function is decreasing on its domain.
The graph: