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!

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

    2(s+5)/(1.25*s^2+3s+9)

    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
    (1-19i/12)/(s+6/5-12i/5)+(1+19i/12)/(s+6/5+12i/5)

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

    thanks
     
  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
    thanks,
    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

    gabbagabbahey

    User Avatar
    Homework Helper
    Gold Member

    Careful,

    [tex]1.25*s^2+3s+9=\frac{5}{4}\left(s+\frac{6}{5}+\frac{12i}{5}\right)\left(s+\frac{6}{5}-\frac{12i}{5}\right)\neq\left(s+\frac{6}{5}+\frac{12i}{5}\right)\left(s+\frac{6}{5}-\frac{12i}{5}\right)[/itex]
     
  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

    s1,s2=-3+-sqrt(9-45)/(5/2)

    s1,s2=-3+-sqrt(-36)/(5/2)

    s1,s2=-3+-6i/(5/2)
    s1,s2=-6/5+-12i/5

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

    gabbagabbahey

    User Avatar
    Homework Helper
    Gold Member

    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

    gabbagabbahey

    User Avatar
    Homework Helper
    Gold Member

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




Similar Discussions: Expand by Partial Fractions!
  1. Expanding box (Replies: 1)

  2. Partial Coherence (Replies: 1)

  3. Expanding sphere (Replies: 1)

Loading...