# Help expansion

1. Jun 2, 2006

### NEWO

help!!! expansion

hi, I am trying to expand a function and can't seem to do it, if some one can tell me how to do it i would appreciate it trmendously. The following is the function;

f(x)=exp(x)/(exp(x)-1)^2

im guessing it is something simple, but i just can't grasp it.

Thank you for your time

newo

2. Jun 2, 2006

### Staff: Mentor

What do you mean by expand? Do you mean just multiplying out the denominator?

$$f(x) = \frac{e^x}{e^{2x} - 2e^x + 1}$$

3. Jun 2, 2006

### NEWO

im just seing if there is a series expansion for the above, if not then it doesn't matter.

4. Jun 2, 2006

### arildno

Of course there exists a series expansion of that function, why do you ask?

5. Jun 2, 2006

### NEWO

coz i need it, I can't find it!!!!

by the way i have looked for it but my books are limited and im not at uni at the mo so can't go to the library.

6. Jun 2, 2006

### arildno

Well, compute the first few terms of the Taylor series about some point, then!

7. Jun 2, 2006

### arunbg

How about adding and subtracting 1 from the numerator ?

8. Jun 2, 2006

### arildno

Well, it might be simpler to write:
$$f(x)=\frac{d}{dx}\frac{1}{1-e^{x}}$$
and expand the denominator in the differentiand to the degree desired.

9. Jun 4, 2006

### NEWO

its ok after looking through some stuff and asking my dad, lol I suddenly remembered about the taylor series of exp(x)=1+x+x^2/2! etc... and if x=c/a and if a>>c we can negate x^2 term due to being much smaller than the x term hence,

exp(x)---> 1+x

and I get what I needed anyway from that so thats great thanks anyway