5.420 Найдите разность \(\frac{a}{14} - \frac{1}{a}\) при a = 7; a = 8; a = 4.

Найдем разность \(\frac{a}{14} - \frac{1}{a}\) при a = 7; a = 8; a = 4.

1. При а = 7:

\(\frac{7}{14} - \frac{1}{7} = \frac{1}{2} - \frac{1}{7} = \frac{1\cdot7}{2\cdot7} - \frac{1\cdot2}{7\cdot2} = \frac{7}{14} - \frac{2}{14} = \frac{7-2}{14} = \frac{5}{14}\)

2. При а = 8:

\(\frac{8}{14} - \frac{1}{8} = \frac{4}{7} - \frac{1}{8} = \frac{4\cdot8}{7\cdot8} - \frac{1\cdot7}{8\cdot7} = \frac{32}{56} - \frac{7}{56} = \frac{32-7}{56} = \frac{25}{56}\)

3. При а = 4:

\(\frac{4}{14} - \frac{1}{4} = \frac{2}{7} - \frac{1}{4} = \frac{2\cdot4}{7\cdot4} - \frac{1\cdot7}{4\cdot7} = \frac{8}{28} - \frac{7}{28} = \frac{8-7}{28} = \frac{1}{28}\)

Ответ: \(\frac{5}{14}; \frac{25}{56}; \frac{1}{28}\)