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Partial Fraction

  1. Oct 18, 2005 #1
    I`ve been asked to complete the following expresion
    [tex]\frac{x^5}{x^3 - x}[/tex]

    I know i`m supossed to reduce the numerator, but i`m a little stuck getting started.

    The problem i have is how do you reduce [tex]x^5[/tex]?

    is it simply [tex]x^3(x^2)[/tex]? but then how do you get rid of the [tex]x^3[/tex]

    AAHH i`m lost.

    I obviously don`t want you to give me the answer so an example of your choice would be greatly appreciated.

    Cheers
     
    Last edited: Oct 18, 2005
  2. jcsd
  3. Oct 18, 2005 #2

    VietDao29

    User Avatar
    Homework Helper

    You can first divide both denominator and numerator by 'x'. They have 'x' in common. So:
    [tex]\frac{x ^ 5}{x ^ 3 - x} = \frac{x ^ 4}{x ^ 2 - 1}[/tex]
    You can use 'polynomial long division' to reduce the degree of the numerator. You can click here for more information.
    -------------------
    Or you can also do it a little bit differently:
    You notice that x4 = (x2)(x2). But the denominator is x2 - 1, so:
    x4 = x2(x2 - 1) + x2.
    Now:
    [tex]\frac{x ^ 4}{x ^ 2 - 1} = \frac{x ^ 2(x ^ 2 - 1) + x ^ 2}{x ^ 2 - 1} = x ^ 2 + \frac{x ^ 2}{x ^ 2 - 1}[/tex]
    Now just do the same for [tex]\frac{x ^ 2}{x ^ 2 - 1}[/tex]:
    [tex]\frac{x ^ 2}{x ^ 2 - 1} = \frac{x ^ 2 + ... - ...}{x ^ 2 - 1} = ...[/tex]
    Viet Dao,
     
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