SOLUTION: Pls. help to rationalize the numerator for ( ³√x-³√a ) / ( x-a ) (the numberator is cube root x and cube root a)

Algebra ->  Radicals -> SOLUTION: Pls. help to rationalize the numerator for ( ³√x-³√a ) / ( x-a ) (the numberator is cube root x and cube root a)      Log On


   

Question 390574: Pls. help to rationalize the numerator for
( ³√x-³√a ) / ( x-a )
(the numberator is cube root x and cube root a)
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
%28root%283%2Cx%29-root%283%2Ca%29%29%2F%28x-a%29

Let root%283%2Cx%29=y, then x=y%5E3
Let root%283%2Ca%29=z, then a=z%5E3

Substituting:

%28y-z%29%2F%28y%5E3-z%5E3%29

Factor the denominator as the difference of two cubes:

%28y-z%29%2F%28%28y-z%29%28y%5E2%2Byz%2Bz%5E2%29%29

Cancel the %28y-z%29's

%28cross%28y-z%29%29%2F%28%28cross%28y-z%29%29%28y%5E2%2Byz%2Bz%5E2%29%29

1%2F%28y%5E2%2Byz%2Bz%5E2%29

Substitute y=root%283%2Cx%29
Substitute z=root%283%2Ca%29

1%2F%28root%283%2Cx%29%5E2%2Broot%283%2Cx%29root%283%2Ca%29%2Broot%283%2Ca%29%5E2%29


1%2F%28root%283%2Cx%5E2%29%2Broot%283%2Cxa%29%2Broot%283%2Ca%5E2%29%29

Edwin