Results 1 to 6 of 6

Math Help - Partial fraction decomposition

  1. #1
    Newbie
    Joined
    May 2010
    Posts
    20

    Partial fraction decomposition

    How would I find the partial fraction decomposition for 1/((1-x)(1-x^3))?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by thefrog View Post
    How would I find the partial fraction decomposition for 1/((1-x)(1-x^3))?
    Factorise 1 - x^3 using the difference of two cubes formula. Now see that the denominator has a two-fold repeated linear factor and an irreducible queadratic factor. Now write down the partial fractions corresponding to each. Show all your work and say where you're stuck if you need more help.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Mar 2010
    Posts
    993
    Thanks
    244
    Since 1-x^3=(1-x)(1+x+x^2),

    \frac{1}{(1-x)(1-x^3)}=\frac{1}{(1-x)^2(1+x+x^2)}=\frac{1}{(x-1)^2(x^2+x+1)}, and x^2+x+1 is not factorable, so you set

    \frac{1}{(x-1)^2(x^2+x+1)}=\frac{A}{x-1}+\frac{B}{(x-1)^2}+\frac{Cx+D}{x^2+x+1}

    When there's a squared factor in the denominator, you get fractions with squared and unsquared denominator. When there's a non-factorable quadratic in the denominator, you get a linear term in the corresponding numerator.

    - Hollywood

    Edit: Oops - I didn't realize Mr. Fantastic had already posted. So you get two of the same answer.
    Last edited by hollywood; May 19th 2010 at 09:01 PM. Reason: recognize previous post
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    May 2010
    Posts
    20
    So you're saying I should have believed what Mathematica gave me, then?Thanks, but why is this placed in the precalculus forums? Partial Fractions are not precalculus; I learned calculus well before I first met partial fractions.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member
    Joined
    Mar 2010
    Posts
    993
    Thanks
    244
    I also learned partial fractions when I learned how to integrate rational functions (about 2/3 of the way through the first year of calculus).

    But it can be understood with pre-calculus knowledge, so I don't think the thread has to be moved necessarily.

    - Hollywood
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by thefrog View Post
    So you're saying I should have believed what Mathematica gave me, then?Thanks, but why is this placed in the precalculus forums? Partial Fractions are not precalculus; I learned calculus well before I first met partial fractions.
    The rule of thumb is very simple: If the solution of a question does not require calculus then clearly the question does not belong in the Calculus subforum.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Partial Fraction Decomposition.
    Posted in the Pre-Calculus Forum
    Replies: 12
    Last Post: July 29th 2010, 01:38 AM
  2. Partial fraction decomposition
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: August 16th 2009, 06:07 AM
  3. Partial Fraction Decomposition
    Posted in the Pre-Calculus Forum
    Replies: 6
    Last Post: April 8th 2009, 09:13 PM
  4. partial fraction decomposition
    Posted in the Algebra Forum
    Replies: 1
    Last Post: October 21st 2008, 07:12 PM
  5. Partial fraction decomposition
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: September 11th 2007, 03:48 PM

Search Tags


/mathhelpforum @mathhelpforum