6. Решите уравнение: 2 a)3(+x)=+; 7 1 51 6 12 б) (4-x)+=+; 39 125

a) Решим уравнение:

$$\frac{2}{3} + \left(\frac{1}{7} + x\right) = \frac{5}{6} + \frac{1}{12}$$ $$\frac{2}{3} + \frac{1}{7} + x = \frac{10}{12} + \frac{1}{12}$$ $$\frac{14}{21} + \frac{3}{21} + x = \frac{11}{12}$$ $$\frac{17}{21} + x = \frac{11}{12}$$ $$x = \frac{11}{12} - \frac{17}{21}$$ $$x = \frac{11 \cdot 7}{12 \cdot 7} - \frac{17 \cdot 4}{21 \cdot 4}$$ $$x = \frac{77}{84} - \frac{68}{84}$$ $$x = \frac{9}{84}$$ $$x = \frac{3}{28}$$

б) Решим уравнение:

$$ (4 - x) + \frac{1}{5} = \frac{2}{3} + \frac{5}{9}$$ $$ 4 - x + \frac{1}{5} = \frac{6}{9} + \frac{5}{9}$$ $$ 4 - x + \frac{1}{5} = \frac{11}{9}$$ $$ 4 - x = \frac{11}{9} - \frac{1}{5}$$ $$ 4 - x = \frac{11 \cdot 5}{9 \cdot 5} - \frac{1 \cdot 9}{5 \cdot 9}$$ $$ 4 - x = \frac{55}{45} - \frac{9}{45}$$ $$ 4 - x = \frac{46}{45}$$ $$ x = 4 - \frac{46}{45}$$ $$ x = \frac{4 \cdot 45}{45} - \frac{46}{45}$$ $$ x = \frac{180}{45} - \frac{46}{45}$$ $$ x = \frac{134}{45} $$ $$ x = 2 \frac{44}{45}$$

Ответ: a) $$x = \frac{3}{28}$$, б) $$x = 2 \frac{44}{45}$$