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MathGroup Archive 2001

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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg31009] Re: [mg31000] help: rewriting a fraction a/b==c/d + e/f
  • From: BobHanlon at aol.com
  • Date: Tue, 2 Oct 2001 01:20:44 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

In a message dated 2001/10/1 3:06:03 AM, kroosu at tref.nl writes:

>i'm trying the mathematica demo by doing some basic mathematics.
>now i'm stuck at rewritting a fraction.
>could somebody please help me by telling  me how to rewrite:
>
>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?
>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.
>

1/((x-1)(x^2+x+1))  // Apart

(-x - 2)/(3*(x^2 + x + 1)) + 
  1/(3*(x - 1))

1/((x-1)(x^2+x+1)) - (A/(x-1) + (B*x+C)/(x^2+x+1)) // Together

((-A)*x^2 - B*x^2 - A*x + B*x - 
   C*x - A + C + 1)/((x - 1)*
   (x^2 + x + 1))

Numerator[%]

(-A)*x^2 - B*x^2 - A*x + B*x - 
  C*x - A + C + 1

CoefficientList[%, x]

{-A + C + 1, -A + B - C, -A - B}

Solve[Thread[% == 0], {A,B,C}]

{{A -> 1/3, B -> -(1/3), 
   C -> -(2/3)}}


Bob Hanlon
Chantilly, VA  USA


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