Question 1110967
I think this is what you want:  (you can use 'show source' to see how to format):
{{{ (3+ root(3,3)) / (root(3,9)) }}}

This is not an equation, it is an expression.   The question must be to rationalize the expression (get rid of as many roots as possible, in particular, from the denominator): 
<pre>
{{{  (3+root(3,3)) / (root(3,9))  }}}

 Multiply top and bottom by {{{root(3,9^2) = 9^(2/3) }}} 

= {{{ ((3+root(3,3)) * (root(3,81) )) / ((root(3,9) * (root(3,81))))  }}}   

 Simplify denominator:
= {{{ ((3+root(3,3)) * (root(3,81) )) / 9  }}}   

  Notice that  {{{ root(3,81) = root(3,3^4) }}} 
  Multiply out the numerator, using the above equivalence:
= {{{ (root(3,3^7) +root(3,3^5))  / 9  }}}   

 Factor out a 3 from the numerator and cancel it with one of the 3's in the denominator
  9=3*3 so now the denominator is just 3:  ( 3*Numerator / 9  =  Numerator / 3 )
= {{{ 3(root(3,3^4) +root(3,3^2))  / 9  }}}
   

= {{{ (root(3,3^4) +root(3,3^2))  / 3  }}}   
 
 Expand the contents of the radical signs

= {{{ highlight( (root(3,81) +root(3,9))  / 3 ) }}}   

In many cases, this is considered rationalized, and it can be left in this form.

 
 The only additional step I see that might be needed by your teacher would be to 
 break (A+B)/3  into  A/3 + B/3  because it lowers the exponents under the radical sign:

Starting with
=  {{{ (root(3,3^4)/3) +root(3,3^2)/3  }}}   

= {{{  root(3,3) +  root(3,9)/3 }}}