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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.