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Homework Help: Partial fractions with generating functions

  1. Jun 26, 2010 #1
    Suppose that q(z) = 1, and p(z) = (1 + z)(1 + 3z).

    We wish to express q(z)/p(z) in the form

    where A and B are constants. To find them, we multiply through by p(z) =
    (1 + z)(1 + 3z) and obtain
    1 = A(1 + 3z) + B(1 + z)
    = (A + B) + (3A + B)z

    Im fine up to this point, But according to my notes it is obvious that A + B = 1 and (3A + B)z = 0.

    I can not see why this is the case?

    Any help would be greatly appreciated.
     
  2. jcsd
  3. Jun 26, 2010 #2
    Never mind figured it out:

    1 + 0*z = ....
     
  4. Jun 26, 2010 #3

    Hurkyl

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    Staff Emeritus
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    Gold Member

    Two polynomials are equal iff their coefficients are equal.
     
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