(\(\frac{3\sqrt6 + \sqrt{54}}{\sqrt5(3\sqrt5)})^{-1}\)

= \(\frac{√5(3√5)}{3√6 + 3√6}\)

= \(\frac{3*5}{6√6} = \frac{5}{2√6}\)

= \(\frac{5*2√6}{2√6+2√6} = \frac{10√6}{4*6}\)

= \(\frac{5√6}{12}\)