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[tex] \frac{2 \sqrt{2} }{4 - 3 \sqrt{2} } = \frac{2 \sqrt{2} }{4 - 3 \sqrt{2} } \times \frac{4 + 3 \sqrt{2} }{4 + 3 \sqrt{2} } = \frac{2 \sqrt{2}(4 + 3 \sqrt{2}) }{(4 - 3 \sqrt{2})(4 + 3 \sqrt{2} ) } = \frac{8 \sqrt{2} + 6 \times 2 }{16 - 9 \times 2} = \frac{8 \sqrt{2} + 12 }{16 - 18} = \frac{8 \sqrt{2} + 12 }{ - 2} = - 4 \sqrt{2} - 6[/tex]
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