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Re: rationalize numerator of quotient

• To: mathgroup at smc.vnet.net
• Subject: [mg81174] Re: [mg81125] rationalize numerator of quotient
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Fri, 14 Sep 2007 03:45:19 -0400 (EDT)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• References: <29319569.1189724898261.JavaMail.root@eastrmwml14.mgt.cox.net>
• Reply-to: murray at math.umass.edu

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.


Bob Hanlon wrote:
> y = (Sqrt[x] - 2)/(x - 4);
> 
> y // Simplify
> 
> 1/(Sqrt[x] + 2)
> 
> y // Cancel
> 
> 1/(Sqrt[x] + 2)
> 
> y // Apart
> 
> 1/(Sqrt[x] + 2)
> 
> 
> Bob Hanlon
> 
> ---- Murray Eisenberg <murray at math.umass.edu> wrote: 
>> I have a quotient such as:
>>
>>    (Sqrt[x] - 2)/(x-4)
>>
>> I want to "rationalize the numerator" by multiplying numerator and 
>> denominator each by Sqrt[x] + 2 so as to obtain result:
>>
>>    1/(Sqrt[x]+2)
>>
>> How?
>>
>> -- 
>> Murray Eisenberg                     murray at math.umass.edu
>> Mathematics & Statistics Dept.
>> Lederle Graduate Research Tower      phone 413 549-1020 (H)
>> University of Massachusetts                413 545-2859 (W)
>> 710 North Pleasant Street            fax   413 545-1801
>> Amherst, MA 01003-9305
>>
> 

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305