Question

Помогите (30б)
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Answer 1

Ответ:

$1) \frac{ \frac{3}{4} }{ \frac{1}{3}x + \frac{1}{4} } + \frac{2}{3} = 1 \\ \frac{ \frac{3}{4} }{ \frac{1}{3} x + \frac{1}{4} } = 1 - \frac{2}{3} \\ \frac{ \frac{3}{4} }{ \frac{1}{3} x + \frac{1}{4} } = \frac{1}{3} \\ 1 \times ( \frac{1}{3} x + \frac{1}{4} ) = 3 \times \frac{3}{4} \\ \frac{1}{3} x + \frac{1}{4} = \frac{9}{4} \\ \frac{1}{3} x = \frac{9}{4} - \frac{1}{4} \\ \frac{1}{3} x = 2 \\ x = 2 \div \frac{1}{3} \\ x = 2 \times 3 \\ x = 6$

$2) \frac{ \frac{5}{6} }{ \frac{1}{4} x - \frac{7}{12} } - \frac{1}{2} = \frac{3}{14} \\ \frac{ \frac{5}{6} }{ \frac{1}{4} x - \frac{7}{12} } = \frac{3}{14} + \frac{1}{2} \\ \frac{ \frac{5}{6} }{ \frac{1}{4} x - \frac{7}{12} } = \frac{3 + 7}{14} \\ \frac{ \frac{5}{6} }{ \frac{1}{4} x - \frac{7}{12} } = \frac{10}{14} \\ 10 \times (\frac{1}{4} x - \frac{7}{12}) = 14 \times \frac{5}{6} \\ 10 \times \frac{1}{4} x - 10 \times \frac{7}{12} = \frac{14 \times 5}{6} \\ \frac{5}{2} x - \frac{5 \times 7}{6} = \frac{70}{6} \\ \frac{5}{2} x - \frac{35}{6} = \frac{70}{6} \\ \frac{5}{2} x = \frac{70}{6} + \frac{35}{6} \\ \frac{5}{2} x = \frac{105}{6} \\ x = \frac{105}{6} \div \frac{5}{2} \\ x = \frac{105}{6} \times \frac{2}{5} \\ x = 7$

$3) \frac{2 \frac{1}{3} }{ \frac{3}{8}x - \frac{5}{6} } + 5 \frac{2}{3} = 9 \frac{1}{6} \\ \frac{ \frac{2 \times 3 + 1}{3} }{ \frac{3}{8}x - \frac{5}{6} } + \frac{3 \times 5 + 2}{ 3} = \frac{6 \times 9 + 1}{6} \\ \frac{ \frac{7}{3} }{\frac{3}{8}x - \frac{5}{6}} + \frac{17}{3} = \frac{55}{6} \\ \frac{ \frac{7}{3} }{\frac{3}{8}x - \frac{5}{6}} = \frac{55}{6} - \frac{17}{3} \\ \frac{ \frac{7}{3} }{\frac{3}{8}x - \frac{5}{6}} = \frac{55 - 34}{6} \\ \frac{ \frac{7}{3} }{\frac{3}{8}x - \frac{5}{6}} = \frac{21}{6} \\ 21 \times ( \frac{3}{8} x - \frac{5}{6} ) = 6 \times \frac{7}{3} \\ 21 \times \frac{3}{8} x - 21 \times \frac{5}{6} = 14 \\ \frac{63}{8} x - \frac{35}{2} = 14 \\ \frac{63}{8} x = 14 + \frac{35}{2} \\ \frac{63}{8} x = 14 + 17 \frac{1}{2} \\ \frac{63}{8} x = 31 \frac{1}{2} \\ \frac{63}{8} x = \frac{2 \times 31 + 1}{2} \\ \frac{63}{8} x = \frac{63}{2} \\ x = \frac{63}{2} \div \frac{63}{8} \\ x = \frac{63}{2} \times \frac{8}{63} \\ x = 4$