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Simplify the given expressions by rationalizing the denominators.

Mathematical expressions involving rationalizing denominators with square roots.

Mathematical expressions involving rationalizing denominators with square roots.

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Final Answer:
9) $\frac{2\sqrt{2}}{9}$
10) $5\sqrt{2} - 5$
11) $\frac{6(4 - \sqrt{3})}{13}$
12) $-7(2 + \sqrt{5})$
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