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Math Help - simplify this function

  1. #1
    Newbie
    Joined
    Oct 2007
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    18

    simplify this function

    r(s)= ((1+s^2)^-1, root 2 s(1+s^2)^-1, 1- (1+s^2)^-1

    I understand this simplification up to a point:

    r(s)= 1+s^2)^-1 (1, root2 s, s^2) (green i understand, red i dont)

    the (1+s^2)^-1 substitutes nicely for the first 2 sections, but what is the algebra required for the last part?

    I mean s^2 multiplied by (1+s^2)^-1 is equal to 1- (1+s^2)^-1 but I cannot work out how to derive this.

    Can anyone help please?
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  2. #2
    Junior Member
    Joined
    May 2007
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    60
    (1+s^2)^-1 = (1+s^2)^0 - (1+s^2)^-1 = 1/ 1+s^2
    times s^2
    = s^2/ 1+ s^2

    :O
    correct me if I'm wrong
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  3. #3
    Newbie
    Joined
    Oct 2007
    Posts
    18
    Ni hao! and thanks for the help.

    your message:

    (1+s^2)^-1 = 1/ 1+s^2
    times s^2
    = s^2/ 1+ s^2

    ---

    (1+s^2)^-1 = 1/ 1+s^2 - yes understand that
    times s^2 - why?

    how did you know to multiply by s^2 at the end?
    What were the algebraic steps on the run up to that answer?

    feichang ganxing =]
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