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