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Splitting up a fraction

  1. Mar 5, 2012 #1
    I want to split the fraction:

    2a/((a+1)(a2+4))

    I have tried using partial fractions, but came to something that was nonsense, and my question is why that is. Why doesn't partial fractions work in this case, from a mathematical point of view, and is it still possible to split up the fraction?

    ----------------------------------

    Chances are of course that I just used partial fractions the wrong way, so here is how I did:

    2a/((a+1)(a2+4)) = C/(a+1) + D/(a2+4)

    we have that:

    C(a2+4) + D(a+1) = 2a

    Which gives us the equations:

    Ca2 = 0
    4C + D = 0
    Da = 2a

    which clearly contradict each other. What is wrong in my approach?
     
  2. jcsd
  3. Mar 5, 2012 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    You have a quadratic factor, so your template for partial fractions is wrong. You should start from 2a/((a+1)(a^2+4)) = C/(a+1) + (D+Ea)/(a^2+4)
     
  4. Mar 6, 2012 #3
    Sorry, I never really learned about partial fractions, so could you briefly explain why you (as it appears to be) need a polynomial of one degree lower than the denominator's in the numerator?
     
  5. Mar 6, 2012 #4

    Mark44

    Staff: Mentor

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