Evaluating Limits Algebraically: lim x-->-1 (x+1)/(x^2+2x+1)

[track12]

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

when you substitute -1, you get 0/0.
then i tried to factor and cancel out and got 1/x+1 but that still equals 1/0. is the answer that it does not exist or am i doing something wrong?

and also...

lim x-->8 (x^2-64)/(x-9)

it seems like you should factor the top to get (x-8) (x+8) but that doesn't cancel anything out. again, is the answer just 0 or did i do something wrong?

 

[pka]

Re: Evaluating Limits Algebraically

\(\displaystyle \frac{{x + 1}}{{x^2 + 2x + 1}} = \frac{{x + 1}}{{\left( {x + 1} \right)^2 }} = \frac{1}{{\left( {x + 1} \right)}}\;if\;x \ne - 1\)