\(\frac {3 - \sqrt 3}{2 + \sqrt 3} = a + b\sqrt 3\) Rationalize = \(\frac {3 - \sqrt 3}{2 + \sqrt 3} \times \frac {2 - \sqrt 3}{2 - \sqrt 3}\) = \(\frac {(3 - \sqrt 3)}{(2 + \sqrt 3)} \frac {(2 - \sqrt 3)}{(2 - \sqrt 3)}\) = \(\frac {6 - 3 \sqrt 3 - 2 \sqrt 3 + (\sqrt 3)^2}{4 - 2 \sqrt 3 + 2 \sqrt 3 - (\sqrt 3)^2}\) = \(\frac {6 - 5 \sqrt 3 + 3}{4 - 3}\) = \(\frac {9 - 5 \sqrt 3}{1} = 9 - 5 \sqrt 3\) = 9 + (-5) \(\sqrt 3\) \(\therefore a = 9, b = - 5\)