In general, I have no idea how to combine different distributions. I've tried searching online and I've found no general tactic. I know that if you add distributions you can look at the product of the moment generating functions, but other than that no luck. For example,
Imagine Z~exponentla(lambda=1) and W~Gamma(alpha,beta).
Now find the distribution of X=Z/W. I have no idea where to start or really what to do with this.
I would really appreciate a place to look online to understand this problem. Or any books that talk about these methods.