Question 816611
{{{root(3,2)/root(3,6x)}}}
is the same as
{{{root(3,(2/6x))}}}
you can not ever simplify fractions inside of root signs.  That will give you the wrong answer.
{{{root(3,2)/root(3,6x)}}}
To rationalize multiply the top and bottom of the fraction by {{{root(3,6x)}}}.
{{{(root(3,2)*root(3,6x))/6x}}}
{{{root(3, 12x)/6x}}} this is your answer.