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
>

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