Дополнительные упражнения к главе II — К параграфу 6 — 493 — стр. 112

$\frac{1}{11-2\sqrt{30}}-\frac{1}{11+2\sqrt{30}}=\frac{11+2\sqrt{30}-(11-2\sqrt{30})}{(11-2\sqrt{30})(11+2\sqrt{30})}=\frac{4\sqrt{30}}{121-4\cdot 30}=4\sqrt{30}$.

$\frac{5}{3+2\sqrt{2}}+\frac{5}{3-2\sqrt{2}}=5(\frac{1}{3+2\sqrt{2}}+\frac{1}{3-2\sqrt{2}})=5(\frac{3-2\sqrt{2}+3+2\sqrt{2}}{(3+2\sqrt{2})(3-2\sqrt{2})})=\frac{5\cdot 6}{9-4\cdot 2}=30$.

$\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}+\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}=\frac{(\sqrt{5}-\sqrt{3}{)}^2+(\sqrt{5}+\sqrt{3}{)}^2}{(\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3})}=\frac{5-2\sqrt{15}+3+5+2\sqrt{15}+3}{5-3}=\frac{16}{2}=8$.

$\frac{11+\sqrt{21}}{11-\sqrt{21}}+\frac{11-\sqrt{21}}{11+\sqrt{21}}=\frac{(11+\sqrt{21}{)}^2+(11-\sqrt{21}{)}^2}{(11-\sqrt{21})(11+\sqrt{21})}=\frac{121+22\sqrt{21}+21+121-22\sqrt{21}+21}{121-21}=\frac{284}{100}=2,84$.