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Math Help - Help for Partial Fraction

  1. #1
    Member moonnightingale's Avatar
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    Help for Partial Fraction

    Kindly simplify this equation with partial fraction and tell me procedure as well

    3/[s(s+1)(s+3)]

    Thanks
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  2. #2
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      \frac{3}{s(s+1)(s+3) }

     = \frac{3}{ (s+1) ( s^2 + 3s ) }


     = \frac{3}{ (s+1) ( (s+1)(s+2) - 2 )}


     = \frac{1}{2} \left( 3~\frac{s+2 }{ (s+1)(s+2) - 2 } - \frac{3}{  s+1} \right)


     = \frac{1}{2} \left( 3 ~ \frac{s+2}{ s(s+3) } - \frac{3}{ s+1} \right)


     = \frac{1}{2} \left(  ( \frac{2}{s} + \frac{1}{s+3} )  - \frac{3}{ s+1} \right)


     =  \frac{1}{s} + \frac{1}{2 } \frac{1}{s+3} - \frac{3}{2} ~ \frac{1}{s+1}
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  3. #3
    Member moonnightingale's Avatar
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    Thanks a lot for prompt reply.
    How did u perform third step
    1/2( 3 ----------)
    thanks
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  4. #4
    A Plied Mathematician
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    Or, since all the poles are simple, you could use the Heaviside cover-up method.
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  5. #5
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    I regard    s+2 in  (s+1)(s+2) - 2 as a constant a and let X = s+1 so we have

    \frac{2}{X(aX-2 )} = \frac{a}{aX-2} - \frac{1}{X}

     \frac{1}{X(aX-2)} = \frac{1}{2}( \frac{a}{aX-2} - \frac{1}{X}  ) <br />
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