1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Help With Partial Fraction Decomposition

  1. Mar 25, 2012 #1
    1. The problem statement, all variables and given/known data

    I'm supposed to decompose 1 / x(x2 + 1)2
    Also, we haven't learned matrices yet so I can't use that technique to solve it.

    2. Relevant equations

    None.

    3. The attempt at a solution

    1 / x(x2 + 1)2 = A/x + (Bx + C) / (x2 + 1) + (Dx + E) / (x2 + 1)2

    I multiplied everything by the original denominator to get this:
    1 = x3(Bx + C) + x2(A + B + D) + x(C + E) + A

    From that, I can tell that A = 1, and I think that the following should also be true, but I'm not 100% certain:
    B + D = -1
    C + E = 0
    B + C = 0

    So I set x = -1 which gives me
    B - C + 2A + B + D - C - E = 1

    And I know that B + D = -1, so I can write:
    B - 2C + 2A - 1 - E = 1, and since 2A is just 2, I can rewrite everything as
    B - 2C - E = 0
    So I take that and add it to my other equation C + E = 0 to cancel out E, and I get
    B - C = 0, and then add that to my other equation B + C = 0 and then I get 2B = 0, or just
    B = 0, which means D = -1 and C = 0 and E = 0
    My final answer would then be
    1 / x + x / (x2 + 1) - x / (x2 + 1)2

    But that's wrong, because in the answer, only 1 / x is positive. What did I do wrong?
     
  2. jcsd
  3. Mar 25, 2012 #2
    This is where your error is.
    You should get, by multiplying everything by [itex]x(x^2+1)^2[/itex]
    [itex]a(x^2+1)^2 + (bx+c)(x^2+1)x + (dx+e)x = 1[/itex]

    From there expand, equate coefficients etc, and you'll get the right answer.
     
  4. Mar 25, 2012 #3
    Ohhhhhhh I see, thank you!!
     
  5. Mar 26, 2012 #4

    NascentOxygen

    User Avatar

    Staff: Mentor

    Anyone know how to get wolframalpha to solve this with least effort? Would be handy to check the answer.
     
  6. Mar 27, 2012 #5
    Just type in the left hand side and it automatically does a partial fractions decomposition for you (4th box):

    http://www.wolframalpha.com/input/?i=1/(x(x^2+1)^2)
     
  7. Mar 27, 2012 #6

    NascentOxygen

    User Avatar

    Staff: Mentor

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Help With Partial Fraction Decomposition
Loading...