limits w/ 0 as denominator

lim (x^2-3x+2)/(x^2-2x+1)

x->1

i've tried factoring and cancelling but it still gives me a denominator of 0. i worked it out to...

lim (x-2)/(x-1)

x->1

...and got a dead end. then i tried to do some research and found a question much like the above in the text:

lim (x^2-x+6)/(x-2)

x->2

the solution says though that the limit does not exist since x-2->0 (denominator) but x^2-x+6->8 (nominator) as x->2.

that solution is saying that since the nominator and denominator don't agree, the limit doesn't exist.

now back to my first problem using this theory. both the nominator and denominator approach 0 as x->1 so is it correct to say that the limit is therefore 0?

lim (x^2-3x+2)/(x^2-2x+1) = 0??????????

x->1

or did my deadend mean the limit does not exist??

i'd really appreciate any help on this! ... that is if i worded everything so that it's comprehensible. :o