Find the range of f(x)=(x^(2)-9)/(x-3)

I know I could just sub in 2.999 and 3.001 but is there a way to algebraically calculate the range?

So far i have tried: f(x)=((x+3)(x-3))/(x-3)=x+3

f(3)=0 .: range (-infinity,0)U(0,infinity) whereas from my subbing in estimate I obtained range ~ (-infinity,6)U(6,infinity).

Anyone mind helping me out here / nudging me in the right direction?

Thanks in advance.