Partial fraction decomposition

  • Thread starter HorseBox
  • Start date
  • #1
25
0

Homework Statement


[tex]\frac{2x + 2}{x^2 - 2x + 1}dx[/tex]


Homework Equations





The Attempt at a Solution


I factorized the denominator and got [tex]\frac{2x + 2}{(x - 1)^2}[/tex] and I took a look at the solutions manual to see how they handled this but then I see this [tex]\frac{2x + 2}{(x - 1)^2} = \frac{A}{(x - 1)} + \frac{B}{(x - 1)^2}[/tex]. I'm lost how is the denominator of partial fraction B squared?
 

Answers and Replies

  • #2
366
2

Homework Statement


[tex]\frac{2x + 2}{x^2 - 2x + 1}dx[/tex]


Homework Equations





The Attempt at a Solution


I factorized the denominator and got [tex]\frac{2x + 2}{(x - 1)^2}[/tex] and I took a look at the solutions manual to see how they handled this but then I see this [tex]\frac{2x + 2}{(x - 1)^2} = \frac{A}{(x - 1)} + \frac{B}{(x - 1)^2}[/tex]. I'm lost how is the denominator of partial fraction B squared?

That is the rule used when you have degenerate poles (factored terms in the denominator with powers greater than one). The simplest way to understand this is to try and find an equality without following this rule. You will not be able to do it.


Take a look at the following link and note the section on repeated factors in the denominator. The use of this rule ensures that you have enough degrees of freedom to solve for the coefficients in all cases.

http://en.wikipedia.org/wiki/Partial_fraction
 

Related Threads on Partial fraction decomposition

  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
7
Views
733
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
12
Views
910
  • Last Post
Replies
1
Views
2K
  • Last Post
2
Replies
39
Views
5K
  • Last Post
Replies
1
Views
8K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
16
Views
4K
Top