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Re: Algebraic Manipulation

"David Park" <djmp at> wrote in message 
news:<c07p9h$kmc$1 at>...
> 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.

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