4) Simplify. Rationalize the denominator. \( \frac{-\sqrt{3}}{3-\sqrt{6}} \) \( \begin{array}{l}\square \\ \sqrt{\square}\end{array} \)

To simplify and rationalize the denominator of \( \frac{-\sqrt{3}}{3-\sqrt{6}} \), multiply the numerator and denominator by the conjugate of the denominator, \( 3+\sqrt{6} \): \[ \frac{-\sqrt{3}(3+\sqrt{6})}{(3-\sqrt{6})(3+\sqrt{6})} \] Calculating the denominator: \[ (3-\sqrt{6})(3+\sqrt{6}) = 9 - 6 = 3 \] Now, calculate the numerator: \[ -\sqrt{3}(3+\sqrt{6}) = -3\sqrt{3} - \sqrt{18} = -3\sqrt{3} - 3\sqrt{2} \] Putting it all together, we have: \[ \frac{-3\sqrt{3} - 3\sqrt{2}}{3} = -\sqrt{3} - \sqrt{2} \] Thus, the simplified form is: \[ -\sqrt{3} - \sqrt{2} \] In boxed form, your answer looks like this: \( \begin{array}{l} \sqrt{2} \\ \sqrt{3} \end{array} \)