1. **Planteamiento del problema:** Calcular los valores de $B$ y $C$ dados por las expresiones: $$B = 3 + \frac{1 + \frac{2}{2} - 1 \frac{2}{3} + 1 + \frac{\frac{3}{4}}{\frac{9}{6}}}{3 - 3 \frac{1}{2} + \frac{5 \frac{1}{4} + 2}{3 \frac{2}{5} - 1}}$$ $$C = \frac{1 + 3 \frac{5}{7} + 9 \frac{4}{5} + 3 \frac{1}{3} - \frac{10}{14} + \frac{1}{5} + \frac{2}{3}}{\frac{2}{5} + \frac{6}{10}} - 4$$ Luego, encontrar $C - B$. 2. **Conversión de fracciones mixtas a impropias y simplificación:** - $1 \frac{2}{3} = \frac{5}{3}$ - $3 \frac{1}{2} = \frac{7}{2}$ - $5 \frac{1}{4} = \frac{21}{4}$ - $3 \frac{2}{5} = \frac{17}{5}$ - $3 \frac{5}{7} = \frac{26}{7}$ - $9 \frac{4}{5} = \frac{49}{5}$ - $3 \frac{1}{3} = \frac{10}{3}$ 3. **Calcular el numerador de $B$:** $$1 + \frac{2}{2} - \frac{5}{3} + 1 + \frac{\frac{3}{4}}{\frac{9}{6}} = 1 + 1 - \frac{5}{3} + 1 + \frac{3}{4} \times \frac{6}{9}$$ $$= 3 - \frac{5}{3} + \frac{18}{36} = 3 - \frac{5}{3} + \frac{1}{2}$$ 4. **Suma y resta en el numerador de $B$:** $$3 - \frac{5}{3} + \frac{1}{2} = \frac{18}{6} - \frac{10}{6} + \frac{3}{6} = \frac{11}{6}$$ 5. **Calcular el denominador de $B$:** $$3 - \frac{7}{2} + \frac{\frac{21}{4} + 2}{\frac{17}{5} - 1} = 3 - \frac{7}{2} + \frac{\frac{21}{4} + \frac{8}{4}}{\frac{17}{5} - \frac{5}{5}} = 3 - \frac{7}{2} + \frac{\frac{29}{4}}{\frac{12}{5}}$$ 6. **Simplificar la fracción en el denominador de $B$:** $$\frac{29}{4} \div \frac{12}{5} = \frac{29}{4} \times \frac{5}{12} = \frac{145}{48}$$ 7. **Sumar y restar en el denominador de $B$:** $$3 - \frac{7}{2} + \frac{145}{48} = \frac{144}{48} - \frac{168}{48} + \frac{145}{48} = \frac{121}{48}$$ 8. **Calcular $B$ completo:** $$B = 3 + \frac{\frac{11}{6}}{\frac{121}{48}} = 3 + \frac{11}{6} \times \frac{48}{121} = 3 + \frac{528}{726}$$ Simplificamos $\frac{528}{726}$ dividiendo numerador y denominador por 6: $$\frac{\cancel{528}^{88}}{\cancel{726}^{121}}$$ Entonces: $$B = 3 + \frac{88}{121} = \frac{363}{121} + \frac{88}{121} = \frac{451}{121}$$ 9. **Calcular el numerador de $C$:** $$1 + \frac{26}{7} + \frac{49}{5} + \frac{10}{3} - \frac{10}{14} + \frac{1}{5} + \frac{2}{3}$$ Encontramos común denominador 210: $$\frac{210}{210} + \frac{780}{210} + \frac{2058}{210} + \frac{700}{210} - \frac{150}{210} + \frac{42}{210} + \frac{140}{210} = \frac{3780}{210}$$ 10. **Calcular el denominador de $C$:** $$\frac{2}{5} + \frac{6}{10} = \frac{4}{10} + \frac{6}{10} = 1$$ 11. **Calcular $C$ completo:** $$C = \frac{3780}{210} - 4 = 18 - 4 = 14$$ 12. **Calcular $C - B$:** $$C - B = 14 - \frac{451}{121} = \frac{1694}{121} - \frac{451}{121} = \frac{1243}{121}$$ **Respuesta final:** $$C - B = \frac{1243}{121}$$