3*. Вычислите: \((\frac{1}{12} - \frac{1}{13}) : (\frac{1}{13} - \frac{1}{14}) \cdot (\frac{1}{14} - \frac{1}{15}) : (\frac{1}{15} - \frac{1}{16})\)

3*. Вычислите: \((\frac{1}{12} - \frac{1}{13}) : (\frac{1}{13} - \frac{1}{14}) \cdot (\frac{1}{14} - \frac{1}{15}) : (\frac{1}{15} - \frac{1}{16})\)

1) \(\frac{1}{12} - \frac{1}{13} = \frac{13 - 12}{12 \cdot 13} = \frac{1}{156}\)

2) \(\frac{1}{13} - \frac{1}{14} = \frac{14 - 13}{13 \cdot 14} = \frac{1}{182}\)

3) \(\frac{1}{14} - \frac{1}{15} = \frac{15 - 14}{14 \cdot 15} = \frac{1}{210}\)

4) \(\frac{1}{15} - \frac{1}{16} = \frac{16 - 15}{15 \cdot 16} = \frac{1}{240}\)

5) \(\frac{1}{156} : \frac{1}{182} = \frac{1}{156} \cdot \frac{182}{1} = \frac{182}{156} = \frac{91}{78} = \frac{7}{6}\)

6) \(\frac{1}{210} : \frac{1}{240} = \frac{1}{210} \cdot \frac{240}{1} = \frac{240}{210} = \frac{24}{21} = \frac{8}{7}\)

7) \(\frac{7}{6} \cdot \frac{8}{7} = \frac{7 \cdot 8}{6 \cdot 7} = \frac{8}{6} = \frac{4}{3} = 1\frac{1}{3}\)

Ответ: \(1\frac{1}{3}\)