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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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