Re: Question

*To*: mathgroup at smc.vnet.net*Subject*: [mg25265] Re: [mg25258] Question*From*: Andrzej Kozlowski <andrzej at tuins.ac.jp>*Date*: Sun, 17 Sep 2000 17:33:34 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

on 00.9.17 5:47 PM, Steven Spear at smitsky at mindspring.com wrote: > Hi, can anyone be so kind as to tell me how this problem: > > 1/cbrt(m) +2 (One over the Cube Root of "m" plus Two) > > ...can be solved in Mathematica by rationalizing the denominator? Thank you. > Steve > > > > As long as your m is a number the following will work for roots of degree less than 5: RationalizeDenominator1[expr_] := FullSimplify[expr, ComplexityFunction -> ( Count[#, _? (MatchQ[Denominator[#], Power[_, _Rational] _. + _.] &), {0, Infinity} ] + If[FreeQ[#, Root], 0, 1] & ) ] For example: In[3]:= RationalizeDenominator1[1/(3^(1/3) + 2)] Out[3]= 1 1/3 2/3 -- (4 - 2 3 + 3 ) 11 or In[4]:= RationalizeDenominator1[1/(7^(1/4) - 3)] Out[4]= 1 -- (-27 - 3 Sqrt[7] - Sqrt[2 (63 + 44 Sqrt[7])]) 74 It can also be one for expressions involving roots of degree higher than 5 but it is considerably more complicated. In fact already once explained how to do this in this list (in 1999). -- Andrzej Kozlowski Toyama International University JAPAN http://platon.c.u-tokyo.ac.jp/andrzej/ http://sigma.tuins.ac.jp/