Proving the partial fractions formula from residues

[ehrenfest]

Homework Statement

http://books.google.com/books?id=qF...ts=YKlIl_yPb3&sig=MC2QCtuBii9za-vd4FkAJadZ_dI
I am working on 4.3.23b)

I can get that

$$\sum_{i=1}^n \frac{g(x_i)}{f'(x_i)}\frac{1}{x-x_i} = g(x)/f(x)$$

but I do not know where to go from there?

Homework Equations

The Attempt at a Solution

 

[HallsofIvy]

There are several thing mentioned on the page you give. What exactly are you trying to do?

 

[ehrenfest]

I am working on 4.3.23b.