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Math Help - partial fraction did wrongly...

  1. #1
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    partial fraction did wrongly...

    Hi pals , possible to check where did i went wrong ?

    2 / s(1 + s^2) = A/s + B/(1 + s^2)

    then , 2 = A(1 + s^2) + Bs

    when s = 0 , A = 2
    when s = 1 and A = 2 , B = -2

    however i could not get B = -2s

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  2. #2
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    Quote Originally Posted by xcluded View Post
    Hi pals , possible to check where did i went wrong ?

    2 / s(1 + s^2) = A/s + B/(1 + s^2)

    then , 2 = A(1 + s^2) + Bs

    when s = 0 , A = 2
    when s = 1 and A = 2 , B = -2

    however i could not get B = -2s

    Tt should be

    \frac{2}{s(s^2+1)} = \frac{A}{s} + \frac{Bs+C}{s^2+1}.
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  3. #3
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    Quote Originally Posted by Danny View Post
    Tt should be

    \frac{2}{s(s^2+1)} = \frac{A}{s} + \frac{Bs+C}{s^2+1}.
    hmm why Bs + C ?
    Sorry , i'm pretty poor in these.
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  4. #4
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    Quote Originally Posted by xcluded View Post
    hmm why Bs + C ?
    Sorry , i'm pretty poor in these.
    Because the denominator is an "irreducible" (unfactorable in terms of real numbers) quadratic. If x- a is a factor of the denominator, the partial fractions expansion will include \frac{A}{x- a}. If x^2+ cx+ d= (x-a)^2+ b, so that it is irreducible, then the partial fractions expansion will include \frac{Ax+ B}{(x-a)^2+ b}. If the denominator has (x-a)^n as a factor, the partial fraction expansion will include \frac{A_1}{x-a}+ \frac{A_2}{(x-a)^2}+ \cdot\cdot\cdot+ \frac{A_n}{(x-a)^n}. Finally, if the denominator has (x^2+ a)^n as a factor, the partial fraction expansion will include \frac{A_1x+ B_1}{x^2+ a}+ \frac{A_2x+ B_2}{(x^2+a)^2}+ \cdot\cdot\cdot+  \frac{A_nx+ B_n}{(x^2+a)^n}.

    Since any polynomial, with real coefficients, can be factored (in the real numbers) to powers of linear or powers of quadratic terms, those are all the terms you need.
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