Re: Simplifying Expressions with Ratios of Factors

*To*: mathgroup at smc.vnet.net*Subject*: [mg48583] Re: [mg48579] Simplifying Expressions with Ratios of Factors*From*: Selwyn Hollis <sh2.7183 at misspelled.erthlink.net>*Date*: Sat, 5 Jun 2004 19:58:05 -0400 (EDT)*References*: <200406051119.HAA11825@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

On Jun 5, 2004, at 7:19 AM, David Park wrote: > 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/ > David, This is totally ad hoc, but it works: Simplify[expr1 /. m -> 2*\[Rho]*c] /. c -> m/(2*\[Rho]) ----- Selwyn Hollis http://www.math.armstrong.edu/faculty/hollis (edit reply-to to reply)

**References**:**Simplifying Expressions with Ratios of Factors***From:*"David Park" <djmp@earthlink.net>