annoying limit problem

[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.

[D H]

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?

[EvilBunny]

I don't really see how further I can simplyfy

numerator is

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

[D H]

Find the common factor.

[EvilBunny]

I don't see a common factor in

1/b - 1/3

or

b-3

[dynamicsolo]

(1/b) - (1/3)



How do you take the difference of two fractions?

[EvilBunny]

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

[EvilBunny]

well am still stuck.


So I put them on the same denominator and end with


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

[EvilBunny]

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