simplifying limit: lim, t->1, (3-2t-t^2)/(t-1) = lim, ....

[blackhat]

OK, I'm having a problem following the logic on this problem:

lim (3 -2t - t^2)/(t-1) = lim -t^2 - t -3
t->1 t->1

how did they simplify the limit?

Thanks in advance.

 

[wjm11]

Re: a simple problem

OK, I'm having a problem following the logic on this problem:

lim (3 -2t - t^2)/(t-1) = lim -t^2 - t -3
t->1 t->1

how did they simplify the limit?

Factor and simplify:
(3 -2t - t^2)/(t-1) = -(t^2 + 2t –3)/(t – 1) = -(t + 3)(t – 1)/ (t – 1) = -(t + 3)

Hope that helps.