Re: Simplify Question
- To: mathgroup at smc.vnet.net
- Subject: [mg41671] Re: Simplify Question
- From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
- Date: Fri, 30 May 2003 03:56:18 -0400 (EDT)
- Organization: Universitaet Leipzig
- References: <bb4uq3$43d$1@smc.vnet.net>
- Reply-to: kuska at informatik.uni-leipzig.de
- Sender: owner-wri-mathgroup at wolfram.com
Hi,
do you like the output of
Sqrt[2]/Sqrt[1 + 1/x] //
FullSimplify[#, x > 0,
ComplexityFunction -> (If[Head[#] === Rational, 1, 0] &)] &
more ??
Regards
Jens
Dana DeLouis wrote:
>
> Hello. Could someone offer an explanation or a solution on the following? I am trying to simplify an equation that has a Sqrt in both the numerator and denominator. I would like to have just one Sqrt function.
>
> Sqrt[2]/Sqrt[1 + 1/x]
> Returns...
> Sqrt[2]/Sqrt[1 + 1/x]
>
> I am aware that one has to be careful when simplifying Sqrt functions.
> However, I know that x will always be greater than zero, so I thought this would work.
>
> FullSimplify[Sqrt[2]/Sqrt[1 + 1/x], x > 0]
> Returns the same equation...
> Sqrt[2]/Sqrt[1 + 1/x]
>
> I even mention that x is Real...
> FullSimplify[Sqrt[2]/Sqrt[1 + 1/x], x > 0 && Element[x,Reals]]
> Sqrt[2]/Sqrt[1 + 1/x]
>
> I still get a Sqrt over a Sqrt
>
> However, if I change the number 2 in the numerator to a variable say t, to represent two, then it works...
>
> FullSimplify[Sqrt[t]/Sqrt[1 + 1/x], x > 0]
> Sqrt[(t*x)/(1 + x)]
>
> The above has only 1 Sqrt function. :>)
> I can't seem to simplify the above by keeping 2 as 2, and not as a variable (t).
>
> Help on FullSimplify has an example of a Sqrt in both the numerator and denominator. The help example did not make any assumptions on x.
>
> FullSimplify[Sqrt[(2 - x)/(3 + x)]/Sqrt[2 - x]]
>
> Sqrt[1/(3 + x)]
>
> Thank you in advance. This simple example has caused me a lot of grief.
>
> --
> Dana DeLouis
> Windows XP
> Mathematica $VersionNumber -> 4.2
> ng_only at hotmail.com
>
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