To rationalize the denominator when the denominator is the 
difference of cube roots, you must use the factorization of 
the difference of cubes formula.



But write the left side on the right and vice-versa, so you
can better see what to do:



Let A and B be the terms of the denominator:

, 

Substituting into ,



Simplifying,



So as you can see from that, to rationalize the denominator,
you must multiply top and bottom by 



which can be simplified a little:





We have just finished multiplying the bottom by that 
and gotten the rational expression .

Now we must multiply the numerator, which is

 

by it too:

=



=

Combine like terms:



Now put this over the denominator which we rationalized
first:



Edwin