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 > > = = = = = = = = = = = = = = = = =