Simplify the expression: 18 / (3 + sqrt(3)) + 3 * sqrt(3)

1. Rationalize the denominator of the first term:
(18 / (3 + sqrt(3))) * ((3 - sqrt(3)) / (3 - sqrt(3))) = (18 * (3 - sqrt(3))) / (9 - 3) = (18 * (3 - sqrt(3))) / 6 = 3 * (3 - sqrt(3)) = 9 - 3*sqrt(3).
2. Add the second term:
(9 - 3*sqrt(3)) + 3*sqrt(3) = 9.
3. The simplified expression is 9.