\(\left\(15\frac{1}{3}-8\frac{5}{18}\right\):\(\frac{4}{7}\):6-\(\frac{1}{21}\)-\(\frac{5}{8}\)

Решение:

1. \( 15\frac{1}{3} = \frac{46}{3} \)
2. \( 8\frac{5}{18} = \frac{149}{18} \)
3. \( \frac{46}{3} - \frac{149}{18} = \frac{46 \cdot 6 - 149}{18} = \frac{276 - 149}{18} = \frac{127}{18} \)
4. \( \frac{127}{18} : \frac{4}{7} = \frac{127}{18} \cdot \frac{7}{4} = \frac{889}{72} \)
5. \( \frac{889}{72} : 6 = \frac{889}{72 \cdot 6} = \frac{889}{432} \)
6. \( \frac{889}{432} - \frac{1}{21} - \frac{5}{8} \)
7. \( \text{LCM}(432, 21, 8) = \text{LCM}(2^4 \cdot 3^3, 3 \cdot 7, 2^3) = 2^4 \cdot 3^3 \cdot 7 = 16 \cdot 27 \cdot 7 = 3024 \)
8. \( \frac{889 \cdot 7}{3024} - \frac{1 \cdot 144}{3024} - \frac{5 \cdot 378}{3024} = \frac{6223 - 144 - 1890}{3024} = \frac{4189}{3024} \)

Ответ: \(\frac{4189}{3024}\)