woh!! lol! coooool!!!
i completely missed the fact that (x-3)(x+1)/(x-3) = 0*(x+1)/0 at x = 3!
holy doo doo crap!
man, i'm excited lol. you just cleared up a weak of function limit confusion right there!

another question. 0/0 is indeterminate. someone explained it like this

0*1 = 0 so 0/0 = 1
0*2 = 0 so 0/0 = 2
...

and so we conclude that 0/0 is indeterminate (rather than undefined)

is this really correct way of thinking about it? i mean, if 0/0 can equal any real number, and shouldn't 0/0 = inf.
I know there was that post on dividing by 0, but i think my question is different.