Question

Use algebra to evaluate the limit exactly.

lim(h->0) : (1/(3+h) - (1/3))/h

Answer 1

find the common denominator for the top:
1/(3+h) - (1/3) = (3-(3+h))/(3(3+h))

Answer 2

So on top you have:
-h/(3(3+h))
on the bottom you have:
h
The whole limit becomes:
-1/(3(3+h))

Answer 3

Now plug in h=0 to get -1/9