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Re: Simplifying Expressions with Ratios of Factors

• To: mathgroup at smc.vnet.net
• Subject: [mg48584] Re: [mg48579] Simplifying Expressions with Ratios of Factors
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Sat, 5 Jun 2004 19:58:05 -0400 (EDT)
• References: <200406051119.HAA11825@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

On 5 Jun 2004, at 20:19, 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


Since you do not show us the way that "does not totally please you", it 
is difficult to judge what sort of thing would. The most obvious 
approach that comes ot my mind is, at least in my opinion, very simple:


Cancel /@ (expr1 /. m -> k*$B&Q(B) /. k -> m/$B&Q(B

This diffeers slightly from your expr2 but it does not seem to me worth 
any further effort to remove this difference.

Andrzej


Andrzej Kozlowski
Chiba, Japan
http://www.mimuw.edu.pl/~akoz/

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