3*. Вычислите: \(\left(\frac{1}{14}-\frac{1}{15}\right):\left(\frac{1}{15}-\frac{1}{16}\right)\cdot\left(\frac{1}{16}-\frac{1}{17}\right):\left(\frac{1}{17}-\frac{1}{18}\right)\).

Question

3*. Вычислите: \(\left(\frac{1}{14}-\frac{1}{15}\right):\left(\frac{1}{15}-\frac{1}{16}\right)\cdot\left(\frac{1}{16}-\frac{1}{17}\right):\left(\frac{1}{17}-\frac{1}{18}\right)\).

Accepted Answer

Вычислим разности дробей:

\(\frac{1}{14}-\frac{1}{15}=\frac{1}{210}\), \(\frac{1}{15}-\frac{1}{16}=\frac{1}{240}\), \(\frac{1}{16}-\frac{1}{17}=\frac{1}{272}\), \(\frac{1}{17}-\frac{1}{18}=\frac{1}{306}\).

Тогда:

\[\frac{1}{210}:\frac{1}{240}\cdot\frac{1}{272}:\frac{1}{306}=\frac{240}{210}\cdot\frac{306}{272}=\frac{8}{7}\cdot\frac{153}{136}=\frac{9}{7}.\]

Ответ: \(\frac{9}{7}\).