       Re: Partial fraction command

• To: mathgroup at smc.vnet.net
• Subject: [mg52674] Re: [mg52663] Partial fraction command
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Tue, 7 Dec 2004 05:48:31 -0500 (EST)
• References: <200412070910.EAA09230@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```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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