Задание 3. Найдите значение выражения: 1) \frac{1}{\frac{1}{30} + \frac{1}{42}} 2) \frac{1}{\frac{1}{36} - \frac{1}{44}} 3) \frac{1}{\frac{1}{36} + \frac{1}{45}} 4) \frac{1}{\frac{1}{35} - \frac{1}{60}} 5) \frac{1}{\frac{1}{21} + \frac{1}{28}} 6) \frac{1}{\frac{1}{72} - \frac{1}{99}} 7) 10 \cdot (\frac{1}{5})^2 - 12 \cdot \frac{1}{5} 8) 8 \cdot (\frac{1}{4})^2 - 14 \cdot \frac{1}{4} 9) 21 \cdot (\frac{1}{7})^2 - 10 \cdot \frac{1}{7} 10) 6 \cdot (\frac{1}{3})^2 - 17 \cdot \frac{1}{3} 11) 18 \cdot (\frac{1}{9})^2 - 20 \cdot \frac{1}{9} 12) 15 \cdot (\frac{1}{5})^2 - 8 \cdot \frac{1}{5}

Решение: 1) \frac{1}{\frac{1}{30} + \frac{1}{42}} = \frac{1}{\frac{42 + 30}{30 \cdot 42}} = \frac{1}{\frac{72}{1260}} = \frac{1260}{72} = \frac{630}{36} = \frac{315}{18} = \frac{105}{6} = \frac{35}{2} = 17.5 2) \frac{1}{\frac{1}{36} - \frac{1}{44}} = \frac{1}{\frac{44 - 36}{36 \cdot 44}} = \frac{1}{\frac{8}{1584}} = \frac{1584}{8} = 198 3) \frac{1}{\frac{1}{36} + \frac{1}{45}} = \frac{1}{\frac{45 + 36}{36 \cdot 45}} = \frac{1}{\frac{81}{1620}} = \frac{1620}{81} = 20 4) \frac{1}{\frac{1}{35} - \frac{1}{60}} = \frac{1}{\frac{60 - 35}{35 \cdot 60}} = \frac{1}{\frac{25}{2100}} = \frac{2100}{25} = 84 5) \frac{1}{\frac{1}{21} + \frac{1}{28}} = \frac{1}{\frac{28 + 21}{21 \cdot 28}} = \frac{1}{\frac{49}{588}} = \frac{588}{49} = 12 6) \frac{1}{\frac{1}{72} - \frac{1}{99}} = \frac{1}{\frac{99 - 72}{72 \cdot 99}} = \frac{1}{\frac{27}{7128}} = \frac{7128}{27} = 264 7) 10 \cdot (\frac{1}{5})^2 - 12 \cdot \frac{1}{5} = 10 \cdot \frac{1}{25} - \frac{12}{5} = \frac{10}{25} - \frac{12}{5} = \frac{2}{5} - \frac{12}{5} = \frac{-10}{5} = -2 8) 8 \cdot (\frac{1}{4})^2 - 14 \cdot \frac{1}{4} = 8 \cdot \frac{1}{16} - \frac{14}{4} = \frac{8}{16} - \frac{14}{4} = \frac{1}{2} - \frac{7}{2} = \frac{-6}{2} = -3 9) 21 \cdot (\frac{1}{7})^2 - 10 \cdot \frac{1}{7} = 21 \cdot \frac{1}{49} - \frac{10}{7} = \frac{21}{49} - \frac{10}{7} = \frac{3}{7} - \frac{10}{7} = \frac{-7}{7} = -1 10) 6 \cdot (\frac{1}{3})^2 - 17 \cdot \frac{1}{3} = 6 \cdot \frac{1}{9} - \frac{17}{3} = \frac{6}{9} - \frac{17}{3} = \frac{2}{3} - \frac{17}{3} = \frac{-15}{3} = -5 11) 18 \cdot (\frac{1}{9})^2 - 20 \cdot \frac{1}{9} = 18 \cdot \frac{1}{81} - \frac{20}{9} = \frac{18}{81} - \frac{20}{9} = \frac{2}{9} - \frac{20}{9} = \frac{-18}{9} = -2 12) 15 \cdot (\frac{1}{5})^2 - 8 \cdot \frac{1}{5} = 15 \cdot \frac{1}{25} - \frac{8}{5} = \frac{15}{25} - \frac{8}{5} = \frac{3}{5} - \frac{8}{5} = \frac{-5}{5} = -1