Е) [ (3/5 + 2/7) · 1/17 − (2 − 7/23 − 45/46) ] : 69/80 · 1/3

Решение:

\( \left[ (\frac{3}{5} + \frac{2}{7}) \cdot \frac{1}{17} - (2 - \frac{7}{23} - \frac{45}{46}) \right] : \frac{69}{80} \cdot \frac{1}{3} \)

1. \( \frac{3}{5} + \frac{2}{7} = \frac{21 + 10}{35} = \frac{31}{35} \)
2. \( \frac{31}{35} \cdot \frac{1}{17} = \frac{31}{595} \)
3. \( 2 - \frac{7}{23} - \frac{45}{46} = \frac{92}{46} - \frac{14}{46} - \frac{45}{46} = \frac{92 - 14 - 45}{46} = \frac{33}{46} \)
4. \( \frac{31}{595} - \frac{33}{46} = \frac{31 \cdot 46 - 33 \cdot 595}{595 \cdot 46} = \frac{1426 - 19635}{27370} = \frac{-18209}{27370} \)
5. \( \frac{-18209}{27370} : \frac{69}{80} \cdot \frac{1}{3} = \frac{-18209}{27370} \cdot \frac{80}{69} \cdot \frac{1}{3} = \frac{-18209 \cdot 80}{27370 \cdot 69 \cdot 3} = \frac{-1456720}{6378390} \)

Ответ: \( \frac{-1456720}{6378390} \)