curve sketching clarification

My equation is f(x)=x/x^2-4

So from that, heres what I have gotten so far...

-domain: X is a real number that cannot be 2, -2

- x-intercept is 0

- y intercept is 0

-There is a horizontal asymptote at y=0

-There are vertical asymptotes at x=2 and x=-2

-To find the critical numbers, I have to take the derivative and I did so using the quotient rule and came up with

f'(x)= -2x^2/x^2-4

1) How do I find the critical numbers by setting the function equal to 0? Am i dealing with the numerator? denominator?