420 Найдите разность a/14 - 1/a при a = 7; a = 8; a = 4.

Найдем разность a/14 - 1/a при а = 7; а = 8; а = 4.

1) При а = 7:

$$\frac{a}{14} - \frac{1}{a} = \frac{7}{14} - \frac{1}{7} = \frac{1}{2} - \frac{1}{7} = \frac{1 \cdot 7}{2 \cdot 7} - \frac{1 \cdot 2}{7 \cdot 2} = \frac{7}{14} - \frac{2}{14} = \frac{7-2}{14} = \frac{5}{14}$$

2) При а = 8:

$$\frac{a}{14} - \frac{1}{a} = \frac{8}{14} - \frac{1}{8} = \frac{4}{7} - \frac{1}{8} = \frac{4 \cdot 8}{7 \cdot 8} - \frac{1 \cdot 7}{8 \cdot 7} = \frac{32}{56} - \frac{7}{56} = \frac{32-7}{56} = \frac{25}{56}$$

3) При а = 4:

$$\frac{a}{14} - \frac{1}{a} = \frac{4}{14} - \frac{1}{4} = \frac{2}{7} - \frac{1}{4} = \frac{2 \cdot 4}{7 \cdot 4} - \frac{1 \cdot 7}{4 \cdot 7} = \frac{8}{28} - \frac{7}{28} = \frac{8-7}{28} = \frac{1}{28}$$

Ответ: 5/14; 25/56; 1/28