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Simplifying Expressions with Ratios of Factors


Dear MathGroup,

I can do the following but not in a way that totally pleases me. It exemplifies a common problem of simplifying expressions that contain a ratios of factors that we wish to combine.

What is the best way to simplify expr1 to expr2?

expr1 = d\[Tau]^2 == (dt^2*(m - 2*\[Rho])^2)/(m + 2*\[Rho])^2 - 
    ((m + 2*\[Rho])^4*(d\[Rho]^2 + d\[Theta]^2*\[Rho]^2 + d\[Phi]^2*\[Rho]^2*
        (sin^2*\[Theta])))/(16*\[Rho]^4)


expr2 = d\[Tau]^2 == (dt^2*(m/(2*\[Rho]) - 1)^2)/(m/(2*\[Rho]) + 1)^2 - 
    (m/(2*\[Rho]) + 1)^4*(d\[Rho]^2 + d\[Theta]^2*\[Rho]^2 + 
      d\[Phi]^2*\[Rho]^2*(sin^2*\[Theta]))

David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/ 



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