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Find the partial fraction

  1. Mar 27, 2013 #1
    1. The problem statement, all variables and given/known data
    (x^3+4)/((x^2-1)(x^2+3x+2))


    2. Relevant equations



    3. The attempt at a solution
    Try separating them into Ax+B and Cx+D, then expand until
    (A+C)x3+(3A+B+D)x2+(2A+3B-C)x+(2B-D)
    then, I was stuck. I can't find any value for A,B,C or D. Is my attempt correct or is there other way to solve it?
     
  2. jcsd
  3. Mar 27, 2013 #2

    SteamKing

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    Staff Emeritus
    Science Advisor
    Homework Helper

    Look at your expansion. What must A+C equal to match the original numerator? Follow this line of reasoning for the other factors. You will wind up with a system of equations to solve.
     
  4. Mar 27, 2013 #3

    Mark44

    Staff: Mentor

    Did you factor the denominator? It's not clear to me from your work that you did. The right side should look something like this:
    $$ \frac{A}{x - r_1} + \frac{B}{x - r_2} + \frac{C}{(x - r_2)^2} + \frac{D}{x - r_3}$$
    The reason for the 3rd term above is that there is a repeated factor that is shared by the two quadratics in the denominator.
     
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