Re: Algebraic Manipulation

*To*: mathgroup at smc.vnet.net*Subject*: [mg46197] Re: Algebraic Manipulation*From*: koopman at sfu.ca (Ray Koopman)*Date*: Tue, 10 Feb 2004 00:06:45 -0500 (EST)*References*: <c07p9h$kmc$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

"David Park" <djmp at earthlink.net> wrote in message news:<c07p9h$kmc$1 at smc.vnet.net>... > > I'm always interested in Mathematica techniques for manipulating and simplifying algebraic expressions. I came across the following problem, which I was only able to do with a fair amount of difficulty. > > expr = x*y*(-(z^2/(r^2*(x^2 + y^2))) - 1/(r*(k + r)) + 1/(x^2 + y^2)) > > where > > r^2 == x^2 + y^2 + z^2 > > reduces to > > (k*x*y)/(r^2*(k + r)) > > I wonder if anyone can show an elegant or short method to do the simplification? Together[expr /. x^2+y^2 -> r^2-z^2] gets it for me.