Answer
$ \frac{9-5\sqrt 3}{3} $
Work Step by Step
$\frac{\sqrt 3-1}{2\sqrt 3+3}=\frac{\sqrt 3-1}{2\sqrt 3+3}\times\frac{2\sqrt 3-3}{2\sqrt 3-3}=\frac{6-3\sqrt 3-2\sqrt 3+3}{12-9}=\frac{9-5\sqrt 3}{3} $
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