I should mention that I looked into partial fraction decomposition, but it seemed to be the wrong direction as it doesn't solve my issue with multiple x-terms in the denominator.

I also tried separating the numerator, then factoring out the corresponding exponent in the denominator. This results in two fractions with only one x term in each denominator, but I am unsure how to proceed from there to reduce it further to only one term.

I think if I could get my feet grounded on a correct approach, I could figure it out. Thanks for reading.

Edit: I have solved the problem. Is it possible to write math equations into the forums? If so, I will show mathematically how I did it in case anyone is interested.

In words, I made the following steps:

1. factored e^{-bx}into (e^{-ax})(e^{-cx}). This allowed me to factor out e^{-ax}in both the numerator and denominator and reduced me to two exponential terms.

2. I then factored out C_{1}from the numerator.

3. I simultaneously added and subtracted a C_{1}(C_{3}e^{-cx}) term in the numerator, where I chose C_{3}so that the numerator could be separated to cancel with the denominator. This left me with a non-fraction term and a simplified fraction term with no addition operators in the numerator.

4. Taking the simplified fraction, I factored out e^{-cx}in the numerator and denominator and canceled it out.

This left me with an equation with one x-term as a reciprocal in the denominator. It looks like:

C_{1}+ C_{3}/ (1 + 1 / e^{-cx})