# How do you find the limit of #(1/(x+3)-(1/3))/x# as #x->0#?

##### 1 Answer

Don't think too much about what you should do. Think a lot about what you could do.

#### Explanation:

What do I not like about this?

One thing is the fraction in the numerator of the fraction.

What could I do about it?

Write the top as a single fraction. (Then we'll have a fraction over

Will that help?

Well, we have to try something, so let's do it and if it doesn't help, we'll start over. (It will help.)

# = (3-(x+3))/(3(x+3))# #" "# (still not done)

# = (-x)/(3(x+3))#

Let's see what the big fraction looks like now.

# = ((-x)/(3(x+3)))* 1/x#

# = (-1)/(3(x+3))#

And now we can find the limit as

# = (-1)/(3(0+3)) = (-1)/9#