Power Series expansion of hyperbolic functions

[thanksie037]

Homework Statement

power series expansion of:

((cosh x)/(sinh x)) - (1/x)

Homework Equations

cosh x = (1/2)(e^x + e^-x)
sinh x = (1/2)(e^x - e^-x)

The Attempt at a Solution

what i have so far:

I simplified the first part of the eq to read :
e^2x-1
e^2x-1


now I am stuck. please help

 

[NoMoreExams]

You simplified for it to be \frac{e^{2x}-1}{e^{2x}-1}? Isn't that just 1?

 

[mjsd]

error in simplification:

\frac{e^{2x}+1}{e^{2x}-1}

 

[thanksie037]

I'm sorry that was a typo. Should I just expand both was like you would e^x? how about the 1/x part?

 

[NoMoreExams]

I would and then hopefully things will cancel, for example what's the expansion for e^{2x} - 1?

 

[mjsd]

How do one usually find the taylor series of a given function?
now you have a function, what do you do?