# Homework Help: Annoying limit problem

1. Oct 3, 2007

### EvilBunny

1. The problem statement, all variables and given/known data
1/b - 1/3
-----------
b-3

Lim b ----> 3

2. Relevant equations

3. The attempt at a solution

This is driving me nuts. I always end with 0 but thats not the answer.
I tried direct substitution and it didn't work.

I tried plugging in 2.999999999 but it gives a very small number devided by a very small number

I tried the conjugate and even deviding by the highest power altho thats for infinity.

2. Oct 3, 2007

### D H

Staff Emeritus
You can try this experimentally to see what the limit (if any) appears to be. It takes less than a minute to set this up in an Excel spreadsheet .

You can also try to simplify the expression. What is the numerator?

3. Oct 3, 2007

### EvilBunny

I don't really see how further I can simplyfy

numerator is

1 devided by ''b' minus 1 devided by 3

4. Oct 3, 2007

### D H

Staff Emeritus
Find the common factor.

5. Oct 3, 2007

### EvilBunny

I don't see a common factor in

1/b - 1/3

or

b-3

6. Oct 3, 2007

### dynamicsolo

How do you take the difference of two fractions?

7. Oct 3, 2007

### EvilBunny

woa... nwo seriously how did I miss that. I wasted soo much time on this.

8. Oct 3, 2007

### EvilBunny

well am still stuck.

So I put them on the same denominator and end with

(3-b) / 3 b
-------------
b-3

9. Oct 3, 2007

### EvilBunny

okay -1/9 got it finally . thx for the help