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Re: rationalize numerator of quotient

• To: mathgroup at smc.vnet.net
• Subject: [mg81208] Re: rationalize numerator of quotient
• From: Peter Breitfeld <phbrf at t-online.de>
• Date: Sat, 15 Sep 2007 04:18:06 -0400 (EDT)
• References: <29319569.1189724898261.JavaMail.root@eastrmwml14.mgt.cox.net> <fcdf9p$plc$1@smc.vnet.net>

Murray Eisenberg schrieb:
> Thanks to all who replied, either here or privately.  I didn't try the 
> "obvious" method of using Simplify because, of course, I forgot 
> Mathematica's conception of "simpler".
>
> And this is a good example where Mathematica's "simplify" is contrary to 
> what is taught in school about when a fraction is simpler -- in high 
> school it is often (unfortunately) taught that one should "rationalize" 
> the fraction so that the square-root is in the numerator and never in 
> the denominator.  Of course in calculus, when taking limits of such 
> quotients, that is precisely what you do NOT want to do, but instead 
> want to do what Mathematica's sense of simplifying here accomplishes.
>
[ little bit off-topic ]

I think this is relict of the times roots had to be calculated by
hand. To calculate 1/Sqrt[2] you first had to calculate
Sqrt[2]=1.4142 and then divide 1/1.4142. This is more work to be
done than simply dividing Sqrt[2] by 2.

Gruss Peter
-- 
==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==
Peter Breitfeld, Bad Saulgau, Germany -- http://www.pBreitfeld.de

• Follow-Ups:
  • Re: Re: rationalize numerator of quotient
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>