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. > 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? In[5]:= Apart[1/((x-1)(x^2+x+1)), x] 1 -2 - x Out[5]= ---------- + -------------- 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[6]:= SolveAlways[1/((x-1)(x^2+x+1)) == A/(x-1) + (B*x+C)/(x^2+x+1), x] 1 1 2 Out[6]= {{A -> -, B -> -(-), C -> -(-)}} 3 3 3 Daniel Lichtblau Wolfram Research
- References:
- help: rewriting a fraction a/b==c/d + e/f
- From: kroosu@tref.nl (Okke)
- help: rewriting a fraction a/b==c/d + e/f