[tex] \frac{3 \sqrt{3} }{2 \sqrt{3} + 3 } = \frac{3 \sqrt{3} \times (2 \sqrt{3} - 3) }{(2 \sqrt{3} + 3) \times (2 \sqrt{3} - 3) } = \frac{3 \sqrt{3} \times (2 \sqrt{3} - 3) }{ {(2 \sqrt{3}) }^{2} - {3}^{2} } = \frac{3 \sqrt{3} \times (2 \sqrt{3} - 3) }{4 \times 3 - 9} = \frac{3 \sqrt{3} \times (2 \sqrt{3} - 3) }{12 - 9} = \frac{3 \sqrt{3} \times (2 \sqrt{3} - 3) }{3} = \sqrt{3} \times (2 \sqrt{3} - 3) = \sqrt{3} \times 2 \sqrt{3} - 3 \sqrt{3} = 3 \times 2 - 3 \sqrt{3} = 6 - 3 \sqrt{3} [/tex]
