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$\tt 8) \ \ \ \cfrac{a}{\sqrt{10}}=\cfrac{a\cdot\sqrt{10}}{\sqrt{10}\cdot\sqrt{10}}=\cfrac{a\sqrt{10}}{10}\\\\\\ 9) \ \ \ \cfrac{6}{5\sqrt{7}}=\cfrac{6\cdot\sqrt{7}}{5\sqrt{7}\cdot\sqrt{7}}=\cfrac{6\sqrt{7}}{5\cdot7}=\cfrac{6\sqrt{7}}{35}\\\\\\ 11) \ \ \cfrac{7}{8+3\sqrt{7}}=\cfrac{7(8-3\sqrt{7})}{(8+3\sqrt{7})(8-3\sqrt{7})}=\cfrac{56-21\sqrt{7}}{64-63}=56-21\sqrt{7}$