       Re: help: rewriting a fraction a/b==c/d + e/f

• To: mathgroup at smc.vnet.net
• Subject: [mg31018] Re: [mg31000] help: rewriting a fraction a/b==c/d + e/f
• From: Daniel Lichtblau <danl at wolfram.com>
• Date: Tue, 2 Oct 2001 01:20:54 -0400 (EDT)
• References: <200110010644.CAA24937@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Okke wrote:
>
> hello,
> i'm trying the mathematica demo by doing some basic mathematics.
> now i'm stuck at rewritting a fraction.
>
> 1/((x-1)(x^2+x+1)) to A/(x-1) + (Bx+C)/(x^2+x+1)
> or do i have to do that manualy?

In:= Apart[1/((x-1)(x^2+x+1)), x]
1            -2 - x
Out= ---------- + --------------
3 (-1 + x)               2
3 (1 + x + x )

> and can mathematica find  the values for A, B and C ?
> Solve[eqn1==eq2,{A}] doesnt solve the problem, and subsituting
> x with 1 doesnt either.
>
> tia,
> --
> Okke <kroosu at tref.nl>

You want to find {A,B,C} for which the identity holds for all x. This
may be accomplished with SolveAlways and corrected syntax (Bx is an
"atomic" variable, not equivalent to B*x).

In:= SolveAlways[1/((x-1)(x^2+x+1)) == A/(x-1) + (B*x+C)/(x^2+x+1),
x]
1         1          2
Out= {{A -> -, B -> -(-), C -> -(-)}}
3         3          3

Daniel Lichtblau
Wolfram Research

```

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