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
