3000 / [4 1/8 - 3 1/8 * (4 5/12 - 2 13/24)] + 19:6

Решение:

Выполним действия по порядку:

1. \( 3 \frac{1}{8} = \frac{3 \cdot 8 + 1}{8} = \frac{25}{8} \)
2. \( 4 \frac{5}{12} = \frac{4 \cdot 12 + 5}{12} = \frac{53}{12} \)
3. \( 2 \frac{13}{24} = \frac{2 \cdot 24 + 13}{24} = \frac{61}{24} \)
4. \( \frac{53}{12} - \frac{61}{24} = \frac{53 \cdot 2}{12 \cdot 2} - \frac{61}{24} = \frac{106}{24} - \frac{61}{24} = \frac{45}{24} \)
5. \( \frac{25}{8} \cdot \frac{45}{24} = \frac{25 \cdot 45}{8 \cdot 24} = \frac{1125}{192} \)
6. \( 4 \frac{1}{8} = \frac{4 \cdot 8 + 1}{8} = \frac{33}{8} \)
7. \( \frac{33}{8} - \frac{1125}{192} = \frac{33 \cdot 24}{8 \cdot 24} - \frac{1125}{192} = \frac{792}{192} - \frac{1125}{192} = \frac{-333}{192} \)
8. \( 19 : 6 = \frac{19}{6} \)
9. \( \frac{15}{28} \cdot \left( \frac{-333}{192} \right) + \frac{19}{6} \)
10. \( \frac{15}{28} \cdot \frac{-333}{192} = \frac{15 \cdot -333}{28 \cdot 192} = \frac{-4995}{5376} \)
11. \( \frac{-4995}{5376} + \frac{19}{6} = \frac{-4995}{5376} + \frac{19 \cdot 896}{6 \cdot 896} = \frac{-4995}{5376} + \frac{17024}{5376} = \frac{12029}{5376} \)

Ответ: \( \frac{12029}{5376} \).