2.369 Упростите выражение: 3 a) x + 2 10%-15%;

a) $$\frac{3}{5}x + \frac{2}{15}x - \frac{4}{15}x = \frac{3x \cdot 3}{5 \cdot 3} + \frac{2x}{15} - \frac{4x}{15} = \frac{9x}{15} + \frac{2x}{15} - \frac{4x}{15} = \frac{9x + 2x - 4x}{15} = \frac{7x}{15}$$

в) $$\frac{7}{24}z + (\frac{11}{12}z - \frac{2}{3}z) = \frac{7}{24}z + \frac{11}{12}z - \frac{2}{3}z = \frac{7z}{24} + \frac{11z \cdot 2}{12 \cdot 2} - \frac{2z \cdot 8}{3 \cdot 8} = \frac{7z}{24} + \frac{22z}{24} - \frac{16z}{24} = \frac{7z + 22z - 16z}{24} = \frac{13z}{24}$$

г) $$\frac{9}{14}c - (\frac{3}{14}c + \frac{2}{7}c) = \frac{9}{14}c - \frac{3}{14}c - \frac{2}{7}c = \frac{9c}{14} - \frac{3c}{14} - \frac{2c \cdot 2}{7 \cdot 2} = \frac{9c}{14} - \frac{3c}{14} - \frac{4c}{14} = \frac{9c - 3c - 4c}{14} = \frac{2c}{14} = \frac{c}{7}$$

ж) $$z - \frac{1}{9}z = z - \frac{z}{9} = \frac{z \cdot 9}{9} - \frac{z}{9} = \frac{9z}{9} - \frac{z}{9} = \frac{9z - z}{9} = \frac{8z}{9}$$

з) $$t - \frac{3}{8}t - \frac{7}{8}t = \frac{t \cdot 8}{8} - \frac{3t}{8} - \frac{7t}{8} = \frac{8t}{8} - \frac{3t}{8} - \frac{7t}{8} = \frac{8t - 3t - 7t}{8} = \frac{-2t}{8} = -\frac{t}{4}$$

г) $$\frac{7}{8}x - \frac{5}{6}x = \frac{7x \cdot 3}{8 \cdot 3} - \frac{5x \cdot 4}{6 \cdot 4} = \frac{21x}{24} - \frac{20x}{24} = \frac{21x - 20x}{24} = \frac{x}{24}$$

Ответ: a) $$\frac{7x}{15}$$; г) $$\frac{x}{24}$$; в) $$\frac{13z}{24}$$; г) $$\frac{c}{7}$$; ж) $$\frac{8z}{9}$$; з) $$- \frac{t}{4}$$