Вычислите: а) \(\dfrac{\left(\dfrac75+2\dfrac16\dfrac35\right):\dfrac73}{\left(3:1\dfrac45-\dfrac29\right):\dfrac95}\).

В числителе: \(\left(\frac75+2\frac16\frac35\right):\frac73=\left(\frac75+\frac{13}{5}\right):\frac73=4\cdot\frac37=\frac{12}{7}\).

В знаменателе: \(\left(3:1\frac45-\frac29\right):\frac95=\left(3:\frac95-\frac29\right):\frac95=\left(\frac53-\frac29\right):\frac95=\frac{13}{9}\cdot\frac59=\frac{65}{81}\).

Следовательно, \(\frac{12}{7}:\frac{65}{81}=\frac{972}{455}\).

Ответ: \(\dfrac{972}{455}\).