Dividing Exponential Functions: A Guide

[impendingChaos]

How would one go about dividing two exponential functions.
Basically I have f(x)=k*g(x)
So to solve for k, k=f(x)/g(x)
How would one accomplish this when the functions are both within the format:
A*e^(Cx)+B

Thanks

 

[Eighty]

There's usually no nice simplification when there's a sum in the denominator.

 

[Werg22]

There is a way to simplify, but it's not necessarily what you are looking for. You might or might not end up with an invariant remainder. Here:

$$\frac{Ae^{Cx} + B}{Oe^{Px} + Q}$$

For example, let's say A = 1 and P = 1$$\frac{Ae^{x} + B}{Oe^{x} + Q}$$

Make the substitution e^x = y and get

$$\frac{Ay + B}{Oy + Q}$$

Now we can write

$$\frac{A/O(Oy + Q - Q) + B}{Oy + Q}$$

$$\frac{A/O(Oy + Q ) - QA/O + B}{Oy + Q}$$

$$A/O + \frac{B - QA/O}{Oy + Q}$$

B - QA/O is the remainder here.

 

[impendingChaos]

Hmm I will try your method Werg but like you say I am not sure it is what I am looking for.
I am also trying to make both individual functions into linear expressions by taking the natural log of both sides however I run into natrual log rules which keep this from succeeding. Any ideas in the department?
Another note, I would like to clarify that I should have represented the functions as something like:
f(n)
g(v)
they are both describing different attributes of a system. What I am trying to accomplish is finding a relationship between n and v. Still working towards a solution so any help greatly appreciated.

C.N.