Understanding the Variables in the Couchy Theorem

[transgalactic]

the question and the solution in this link: (you can enlarge by one click on it)
http://img139.imageshack.us/img139/4074/29783975xs2.gif

the key of solving these question is picking the variables
i don't know how they decided to pick those variables?

 

[HallsofIvy]

I can't make heads or tails out of that. You ask "what is the purpose of this process" but I don't see how anyone can tell you that when you haven't said what problem this is supposed to be solving.

 

[transgalactic]

i need to prove the expression
which is located above the astrix

for that they choose h(x) and y(x)
and make couchy theorem on them
i know that its no completely solved
i know what to do once i build the variables

i can't understand by what logic they chose the h(x)=f(x)/g(x) y(x)=1/g(x)??

 

[transgalactic]

they are doing some process on the input expression

(which i need to prove) and after that they chose the variables in a certain way
i can't see what the were trying to do in the process
and what lead them to choose this variables??