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Homework Help: Expand by Partial Fractions!

  1. Oct 16, 2009 #1
    1. The problem statement, all variables and given/known data

    expand by partial fractions:

    2. Relevant equations


    3. The attempt at a solution

    ok I initially used the quadratic formula to get the two roots for the denominator
    these being
    (s+6/5+12i/5)(s+6/5-12i/5) i.e complex numbers

    so now the partial fractions looks like this:

    2(s+5)/(s+6/5+12i/5)(s+6/5-12i/5) = A/(s+6/5+12i/5)+B/(s+6/5-12i/5)

    solving for B I get 1-19/12i which when multiplied by i/i = 1+19i/12 and A is the conjugate I believe, therefore A=1-19i/12

    now the partial fraction looks like this

    does this look right so far? If so how should I proceed in simplifying the terms?

  2. jcsd
  3. Oct 16, 2009 #2
    Multiply the numerator and denominator of each fraction by the complex conjugate of its denominator.
  4. Oct 16, 2009 #3
    have I worked it out right up to the last term?
  5. Oct 16, 2009 #4
    I haven't worked it out, but that suggestion might give you back what you started with.

    Do you need to simplify it?
  6. Oct 16, 2009 #5
    I personally prefer to always leave terms in the most simple of ways.
  7. Oct 16, 2009 #6


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  8. Oct 16, 2009 #7
    I can't see how I've gone wrong. If you use the quadratic formula straight up with
    a=1.25, b=3 and c=9 then




    so s+6/5-12i/5 and s+6/5+12i/5 are the two roots
  9. Oct 16, 2009 #8


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    Sure, the roots are s1,s2=-3+-6i/(5/2), but as^2+bs+c=a(s-s1)(s-s2) not just (s-s1)(s-s2)
  10. Oct 16, 2009 #9
    im getting a little confused now :confused:

    I don't understand why its as^2+bs+c=a(s-s1)(s-s2).
    Is this a special case or something? I have never seen it done like that before

    at this stage... s1,s2=-6/5+-12i/5
    don't you just take the whole term on the right to the left hand side?
    where does the five over four come from here 5/4*(......)?
  11. Oct 16, 2009 #10


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    It's basic algebra.... when you expand (s-s1)(s-s2) using FOIL, you get s^2+bs/a+c/a not as^2+bs+c...you should really know this stuff by now
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