Re: rationalize numerator of quotient
- To: mathgroup at smc.vnet.net
- Subject: [mg81182] Re: rationalize numerator of quotient
- From: Murray Eisenberg <murray at math.umass.edu>
- Date: Fri, 14 Sep 2007 03:49:28 -0400 (EDT)
- Organization: Mathematics & Statistics, Univ. of Mass./Amherst
- References: <fcb3ok$fjj$1@smc.vnet.net> <46E91F86.2080506@gmail.com>
- Reply-to: murray at math.umass.edu
Yes, that does it, thank you. Of course I was hoping there was some way to coerce Mathematica to do it without my explicitly operating upon the numerator and denominator separately. I don't know any English-language term for the operation except something like, "multiply numerator and denominator by the same quantity". (Or, as I like to tell my students: Multiply the fraction by 1. Today 1 is .../.... .) Szabolcs Horv=E1t wrote: > Murray Eisenberg 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? >> > > If you mean doing it automatically for any fraction, then I have no > answer for you ... If you would like to do it manually, then try this: > > expansion[frac_, mul_] := > Expand[Numerator[frac] mul]/(Denominator[frac] mul) > > (What is the operation of multiplying the numerator and denominator by > the same factor called in English? I used the name "expansion" here, a > literal translation from my mother tongue, but I am sure it is not > correct.) > > expansion[(Sqrt[x] - 2)/(x-4), Sqrt[x]+2] > -- 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