Question 390574
<pre>
{{{(root(3,x)-root(3,a))/(x-a)}}}

Let {{{root(3,x)=y}}}, then {{{x=y^3}}}
Let {{{root(3,a)=z}}}, then {{{a=z^3}}}

Substituting:

{{{(y-z)/(y^3-z^3)}}}

Factor the denominator as the difference of two cubes:

{{{(y-z)/((y-z)(y^2+yz+z^2))}}}

Cancel the {{{(y-z)}}}'s

{{{(cross(y-z))/((cross(y-z))(y^2+yz+z^2))}}}

{{{1/(y^2+yz+z^2)}}}

Substitute {{{y=root(3,x)}}}
Substitute {{{z=root(3,a)}}}

{{{1/(root(3,x)^2+root(3,x)root(3,a)+root(3,a)^2)}}}


{{{1/(root(3,x^2)+root(3,xa)+root(3,a^2))}}}

Edwin</pre>