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!

Partial Fractions Explanation

  1. Apr 10, 2014 #1
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    After looking through this on Wiki, I'm a little confused as to how these partial fractions are multiplied out. Is there a rule or something for this?

    With simpler partials I can do it but this one is something else!

    3. The attempt at a solution

    Attached Files:

  2. jcsd
  3. Apr 10, 2014 #2


    User Avatar
    Science Advisor

    The denominator on the left is [tex](x- 1)^3(x^2+ 1)^2[/tex] and every denominator on the right is a factor of that, so multiplying both sides by it will remove all fractions:

    [tex]\frac{2x^6- 4x^5+ 5x^4- 3x^3+ x^2+ 3x}{(x- 1)^3(x^2+ 1)^2}((x-1)^3(x^2+ 1)^2)= 2x^6- 4x^5+ 5x^4- 3x^3+ x^2+ 3x[/tex]

    [tex]\frac{A}{x- 1}((x-1)^3(x^2+ 1)^2)= A(x- 1)^2(x^2+ 1)^2[/tex]
    [tex]\frac{B}{(x- 1)^2}((x-1)^3(x^2+ 1)^2)= B(x- 1)(x^2+ 1)^2[/tex]
    [tex]\frac{C}{(x- 1)^3}((x-1)^3(x^2+ 1)^2)= C(x^2+ 1)^2[/tex]
    [tex]\frac{Dx+ E}{x^2+ 1}((x-1)^3(x^2+ 1)^2)= (Dx+ E)(x- 1)^3(x^2+ 1)[/tex]
    [tex]\frac{Fx+ G}{(x^2+ 1)^2}((x-1)^3(x^2+ 1)^2)= (Fx+ G)(x- 1)^3[/tex]
  4. Apr 10, 2014 #3
    Oh dear, had a complete 'idiot moment'. Thanks dude.

    I've actually been googling trying to find an online differentiation calculator but I'm sure that some of them aren't giving the correct answers- do you know of any which are reliable?
  5. Apr 10, 2014 #4

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

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

Have something to add?
Draft saved Draft deleted