# Small part of a larger problem

1. Sep 12, 2009

### efekwulsemmay

1. The problem statement, all variables and given/known data
I am trying to figure out of $$\frac{9}{x+h}$$ can be split into some thing like
$$\frac{9}{x} + ?$$

2. Relevant equations
None

3. The attempt at a solution
I am not sure what to do. I am trying to do this as part of a larger limits problem.

Last edited: Sep 12, 2009
2. Sep 12, 2009

### Bohrok

I don't believe you can change one to the other. The difference between 9/(x + h) and 9/x is that the first is shifted -h units to the left of the graph of 9/x. 9/x + something would shift the graph of 9/x up something units.

3. Sep 12, 2009

### slider142

You would need to add it to a fraction whose denominator 'a' had the property xa = x + h, or a = (x + h)/x. Unfortunately, there is no fraction that you can add that will not affect the numerator as well.

4. Sep 13, 2009

### efekwulsemmay

Damn, ok thanks for your help, both of you.

5. Sep 14, 2009

### HallsofIvy

Staff Emeritus
What you can do is get a common denominator and subtract fractions.
$$\frac{9}{x+h}- \frac{9}{x}= \frac{9x}{x(x+h)}- \frac{9(x+h)}{x(x+h)}$$
$$= \frac{9x- 9(x+h)}{x(x+h)}= \frac{-9h}{x(x+h)}$$
and you should be able to complete the derivative.

Last edited: Sep 14, 2009
6. Sep 14, 2009

### efekwulsemmay

:surprisedAhhhhh, I see said the blind man to the deaf dog with no ears. Thank you!!!!!

Btw how did you figure out that thats what I was trying to do? That was pretty amazing. :D

Last edited: Sep 14, 2009
7. Sep 14, 2009

### HallsofIvy

Staff Emeritus
Hey, after some time here you get used to figuring out what people are really asking!