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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
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