Сократите дробь: (8 2/3+5*1 1/8-10 :2 2/3)/(8 1/2-5 3/4).

\[\frac{8\frac{2}{3} + 5 \cdot 1\frac{1}{8} - 10\ :2}{8\frac{1}{2} - 5\frac{3}{4}} =\]

\[= \frac{8\frac{2}{3} + 5 \cdot \frac{9}{8} - 5}{\frac{17^{\backslash 2}}{2} - \frac{23}{4}} =\]

\[= \frac{\frac{26^{\backslash 8}}{3} + \frac{45^{\backslash 3}}{8} - 5^{\backslash 24}}{\frac{11}{4}} =\]

\[= \frac{208 + 135 - 120}{24}\ :\frac{11}{4} =\]

\[= \frac{223}{24} \cdot \frac{4}{11} = \frac{223}{66} = 3\frac{25}{66}.\]