4.233 Найдите разность: a) 3/17 – (9/17); б) -8/17 – (-3/17); в) 7/13 – (-1/13); г) 5/14 - 3/7; д) 1/2 - 4/5; e) -2/3 – (-5/6); ж) 3/4 – (-4/9); з) 3/8 – 5/12

a) \(\frac{3}{17} - \frac{9}{17} = \frac{3-9}{17} = \frac{-6}{17} = -\frac{6}{17}\)

б) \(-\frac{8}{17} - (-\frac{3}{17}) = -\frac{8}{17} + \frac{3}{17} = \frac{-8+3}{17} = \frac{-5}{17} = -\frac{5}{17}\)

в) \(\frac{7}{13} - (-\frac{1}{13}) = \frac{7}{13} + \frac{1}{13} = \frac{7+1}{13} = \frac{8}{13}\)

г) \(\frac{5}{14} - \frac{3}{7} = \frac{5}{14} - \frac{3 \cdot 2}{7 \cdot 2} = \frac{5}{14} - \frac{6}{14} = \frac{5-6}{14} = \frac{-1}{14} = -\frac{1}{14}\)

д) \(\frac{1}{2} - \frac{4}{5} = \frac{1 \cdot 5}{2 \cdot 5} - \frac{4 \cdot 2}{5 \cdot 2} = \frac{5}{10} - \frac{8}{10} = \frac{5-8}{10} = \frac{-3}{10} = -\frac{3}{10}\)

e) \(-\frac{2}{3} - (-\frac{5}{6}) = -\frac{2 \cdot 2}{3 \cdot 2} + \frac{5}{6} = -\frac{4}{6} + \frac{5}{6} = \frac{-4+5}{6} = \frac{1}{6}\)

ж) \(\frac{3}{4} - (-\frac{4}{9}) = \frac{3}{4} + \frac{4}{9} = \frac{3 \cdot 9}{4 \cdot 9} + \frac{4 \cdot 4}{9 \cdot 4} = \frac{27}{36} + \frac{16}{36} = \frac{27+16}{36} = \frac{43}{36} = 1\frac{7}{36}\)

з) \(\frac{3}{8} - \frac{5}{12} = \frac{3 \cdot 3}{8 \cdot 3} - \frac{5 \cdot 2}{12 \cdot 2} = \frac{9}{24} - \frac{10}{24} = \frac{9-10}{24} = \frac{-1}{24} = -\frac{1}{24}\)