Results 1 to 5 of 5

Math Help - Partial Fractions with Repeated Roots

  1. #1
    Member
    Joined
    Nov 2009
    Posts
    76

    Partial Fractions with Repeated Roots

    I would appreciate it if somebody could explain why the following applies to partial fractions with repeated roots:

    (x^2-2x+17)/(x+3)(x-1)^2 = A/(x+3)+B/(x-1)+C/(x-1)^2.

    It would make more sense to me if it was as below:

    (x^2-2x+17)/(x+3)(x-1)^2 = A/(x+3)+B/(x-1)+C/(x-1).

    I know this is incorrect however I am unable to find an explanation for why it is done as it is.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Calculus26's Avatar
    Joined
    Mar 2009
    From
    Florida
    Posts
    1,271
    A/(x+3)+B/(x-1)+C/(x-1).
    the least common denominator would be 1/(x+3)(x-1) not 1/(x+3)(x-1)^2 which is what you need



    Think about it the least common denominator of 1/2 + 1/2^2 +1/3

    is 1/(2^2 *3)

    going the other way if you wanted to break 1/(2^2 *3) down into a the most general sum of fractions you would have A/2 + B/2^2 +C/3

    same is true of 1/(x-1)^2(x+3)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,597
    Thanks
    1420
    Quote Originally Posted by p75213 View Post
    I would appreciate it if somebody could explain why the following applies to partial fractions with repeated roots:

    (x^2-2x+17)/(x+3)(x-1)^2 = A/(x+3)+B/(x-1)+C/(x-1)^2.

    It would make more sense to me if it was as below:

    (x^2-2x+17)/(x+3)(x-1)^2 = A/(x+3)+B/(x-1)+C/(x-1).

    I know this is incorrect however I am unable to find an explanation for why it is done as it is.
    Why would that make sense? B/(x-1)+ C/(x-1)= (B+C)/(x-1) so the second fraction adds nothing. And, as Calculus26 told you, after adding the fraction on the right would have denominator (x+3)(x-1), not (x+3)(x-1)^2.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Nov 2009
    Posts
    76
    Thanks for the explanation Calculus26. The light came on but it took a while. Beats me why it is so difficult to find an explanation on the net.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Nov 2009
    Posts
    76
    To Hallsofivy,
    I was looking for help NOT somebody that starts a post with a critical comment like "Why would that make sense". That being the case I would appreciate it if you didn't reply to any of my posts in the future.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Repeated roots
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: October 27th 2010, 04:34 AM
  2. Replies: 7
    Last Post: April 30th 2010, 02:37 PM
  3. Partial Fractions with Repeated Roots
    Posted in the Algebra Forum
    Replies: 6
    Last Post: April 14th 2010, 07:38 AM
  4. repeated roots
    Posted in the Algebra Forum
    Replies: 2
    Last Post: September 7th 2009, 05:51 AM
  5. Replies: 3
    Last Post: June 12th 2009, 11:40 AM

Search Tags


/mathhelpforum @mathhelpforum