Proving continuity multiple ways

The question asks us to prove that
f(x) = {(2x^2-18)/(x+3) if x =/= -3, and -12 if x= -3}
is continuous at Xo = -3

I proved it fairly easily using the epsilon/delta definition, but now have to do it two other ways.
I know one way is to use sequential characterization of limits, but how would I go about using this to show it's continuous?
I think the other way is to use the definition of a limit and show that f(x) has limit F = f(Xo) at Xo, is this correct?
Any help would be appreciated. Thanks!