Re: rationalize numerator of quotient

*To*: mathgroup at smc.vnet.net*Subject*: [mg81167] Re: rationalize numerator of quotient*From*: "David Park" <djmpark at comcast.net>*Date*: Fri, 14 Sep 2007 03:41:41 -0400 (EDT)*References*: <fcb3ok$fjj$1@smc.vnet.net>

The problem is to avoid immediate cancelation of the two factors. There are probably a number of ways. Here are two. MultiplyByOne::usage = "MultiplyByOne[onefactor][expr] will multiply by onefactor and \ expand both the numerator and denominator of expr before \ simplifying."; MultiplyByOne[onefactor_][expr_] := Simplify[Expand[one Numerator[expr]]/Expand[one Denominator[expr]]] (Sqrt[x] - 2)/(x - 4) // MultiplyByOne[Sqrt[x] + 2] 1/(2 + Sqrt[x]) MultiplyByOne::usage = "MultiplyByOne[onefactor][expr] will first multiply expr by \ onefactor and expand, then divide by onefactor and simplidy."; MultiplyByOne[onefactor_][expr_] := With[{work = Expand[onefactor expr]}, Simplify[work/onefactor]] (Sqrt[x] - 2)/(x - 4) // MultiplyByOne[Sqrt[x] + 2] 1/(2 + Sqrt[x]) -- David Park djmpark at comcast.net http://home.comcast.net/~djmpark/ "Murray Eisenberg" <murray at math.umass.edu> wrote in message news:fcb3ok$fjj$1 at smc.vnet.net... >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 >