Division presents a special problem, because if we end up with a limit that equals zero in the denominator of a fraction, the world more or less comes to an end. That sounds like a bad idea to us.
Enough with the pleasantries, here is the Quotient Rule:
If 
and 
then 
given K ≠ 0.
Now that we have the unpleasantries out of the way, we can show you what we mean.
When we have a fraction (i.e., division) within a limit, we can instead find the limits of the top and the bottom on their own.
And we have our answer. We were lucky that the zero was on top of the fraction, and not on the bottom. Soon, though, very soon, we'll be able to find the limits even in that kind of situation. Our limit-finding power will be limitless.