21.
a) [tex]\it ~^{5\sqrt{2} - 4\sqrt{3} )} \frac{1}{5\sqrt{2} + 4\sqrt{3} } + ~^{3\sqrt{2} - 2\sqrt{3} )} \frac{1}{3\sqrt{2} + 2\sqrt{3} } - ~^{4\sqrt{3} - 3\sqrt{2} ) } \frac{10}{4\sqrt{3} + 3\sqrt{2} } = \\ \\ \frac{5\sqrt{2} - 4\sqrt{3} }{(5\sqrt{2} )^{2} - (4\sqrt{3} )^{2} } + \frac{3\sqrt{2} - 2\sqrt{3} }{(3\sqrt{2})^{2} - (2\sqrt{3} )^{2} } - \frac{10(4\sqrt{3} - 3\sqrt{2}) }{(4\sqrt{3})^{2} - (3\sqrt{2})^{2} } = \\ \\ \frac{5\sqrt{2} - 4\sqrt{3} }{50 - 48} + \frac{3\sqrt{2} - 2\sqrt{3} }{18 - 12} - \frac{10(4\sqrt{3} - 3\sqrt{2}) }{48 - 18} = \frac{5\sqrt{2} - 4\sqrt{3} }{2} + \frac{3\sqrt{2} - 2\sqrt{3} }{6} - \frac{10(4\sqrt{3} - 3\sqrt{2}) }{30} = \\ \\ ~^{3)} \frac{5\sqrt{2} - 4\sqrt{3} }{2} + \frac{3\sqrt{2} - 2\sqrt{3} }{6} - ~^{2)} \frac{4\sqrt{3} - 3\sqrt{2} }{3} = \frac{15\sqrt{2 } - 12\sqrt{3} + 3\sqrt{2} - 2\sqrt{3} - 8\sqrt{3} + 6\sqrt{2} }{6} = \\ \\ \frac{24\sqrt{2} - 22\sqrt{3} }{6} = \frac{2(12\sqrt{2} - 11\sqrt{3} ) }{6} = \frac{12\sqrt{2} - 11\sqrt{3} }{3}[/tex]
