...Okay, so I don't understand what I'm doing wrong, so I need some help.

lim x->3 x^2+x-6 / x^2-9

I'm supposed to find the limit, which I can't figure out

straight substitution of x = 3 gets you 6/0 ... what does that tell you about the limit?

Also:

lim x->4- √x -2 / x-4

which is, again, finding the limit.

hint ...

(√x -2)/(x-4) = (√x -2)/[(√x -2)(√x +2)]