Решим пример:
$$\begin{aligned}
8\frac{1}{4} : \left(3\frac{1}{2} + 3\frac{3}{4}\right) + 1 = \frac{33}{4} : \left(\frac{7}{2} + \frac{15}{4}\right) + 1 = \frac{33}{4} : \left(\frac{14 + 15}{4}\right) + 1 = \frac{33}{4} : \frac{29}{4} + 1 = \frac{33}{4} \cdot \frac{4}{29} + 1 = \frac{33}{29} + 1 = 1\frac{4}{29} + 1 = 2\frac{4}{29}
\end{aligned}$$
Ответ: $$2\frac{4}{29}$$