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Re: Partial fraction command


On 7 Dec 2004, at 18:10, Jack and the Beanstalk wrote:
>
> Hello,
>
> Is there any built-in command for partial fraction in Mathematica? eg
>
> (8s + 10)/(s+1)(s+3)^2 = a1/(s+1) + a2/(s+3)^2 +a3/(s+3) to get
> a1,a2,and a3.
>
>

No command will work unless you learn the proper Mathematica syntax. 
But yes, there is a function that will work here:


SolveAlways[(8*s + 10)/((s + 1)*(s + 3)^2) ==
    a1/(s + 1) + a3/(s + 3)^2 + a2/(s + 3), s]


{{a1 -> 1/2, a2 -> -(1/2), a3 -> 7}}

You can also use:


Apart[(8*s + 10)/((s + 1)*(s + 3)^2)]


-(1/(2*(s + 3))) + 7/(s + 3)^2 + 1/(2*(s + 1))


and even


D[Integrate[(8*s + 10)/((s + 1)*(s + 3)^2), s], s]


(1/2)*(-(1/(s + 3)) + 14/(s + 3)^2 + 1/(s + 1))


Andrzej Kozlowski

Chiba, Japan
http://www.akikoz.net/~andrzej/
http://www.mimuw.edu.pl/~akoz/


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