[tex]1. \ \frac{9}{\sqrt{18}}=\frac{9}{\sqrt{9\cdot2}} = \frac{9}{3\sqrt{2}} = \frac{3}{\sqrt{2}}\cdot\frac{\sqrt{2}}{\sqrt{2}} = \frac{3\sqrt{2}}{2}[/tex]
[tex]2. \ \frac{3-2\sqrt{3}}{\sqrt{3}+2} = \frac{(3-2\sqrt{3})(\sqrt{3}-2)}{(\sqrt{3}+2)(\sqrt{3}-2)} = \frac{3\sqrt{3}-6-2\cdot3+4\sqrt{3}}{3-4} = \frac{-12+7\sqrt{3}}{-1} = 12-7\sqrt{3}[/tex]
Oblicz:
[tex]\frac{(2\frac{4}{5}-1,9):3\frac{3}{4}}{(3\frac{1}{6}+1,25)\cdot2,4-5,8}=\frac{(\frac{14}{5}-\frac{19}{10}):\frac{15}{4}}{(\frac{19}{6}+\frac{125}{100})\cdot\frac{24}{10}-\frac{58}{10}}}=\frac{(\frac{28}{10}-\frac{19}{10})\cdot\frac{4}{15}}{(\frac{19}{6}+\frac{5}{4})\cdot\frac{12}{5}-\frac{27}{5}}=\frac{\frac{9}{10}\cdot\frac{4}{15}}{(\frac{38}{12}+\frac{15}{12})\cdot\frac{12}{5}-\frac{27}{5}}=[/tex]
[tex]=\frac{\frac{3}{5}\cdot\frac{2}{3}}{\frac{53}{12}\cdot\frac{12}{5}-\frac{27}{5}} = \frac{\frac{2}{5}}{\frac{53}{5}-\frac{27}{5}}=\frac{2}{5}:\frac{26}{5} = \frac{2}{5}\cdot\frac{5}{26} =\frac{2}{26} = \frac{1}{13}[/tex]
