Simplifying #(3+root(3)3)/root(3)9# means rationalizing the denominator i.e. converting irrational denominator to a rational denominator,

As denominator is #root(3)9=root(3)(3xx3)#, to convert it into a rational number, we need to take everything outside the cube root sign.

However, we could have done so only if we had three #3#'s, but we have only two #3#'s.

Hence, we need to multiply denominator by #root(3)3#, but to keep the expression same, we will have to multiply numerator too by #root(3)3#.

Hence #(3+root(3)3)/root(3)9#

= #(3+root(3)3)/root(3)9xxroot(3)3/root(3)3#

= #(3root(3)3+root(3)3xxroot(3)3)/root(3)27#

= #(3root(3)3+root(3)9)/3#

= #root(3)3+root(3)9/3#