\(\frac{1}{7}\cdot\frac{2}{3}+\frac{5}{6}:\frac{3}{10}-\frac{2}{3}\cdot\frac{3}{7}\)
\(=\left(\frac{1}{7}\cdot\frac{2}{3}-\frac{2}{3}\cdot\frac{3}{7}\right)+\frac{5}{6}\cdot\frac{10}{3}\)
\(=\frac{2}{3}\cdot\left(-\frac{2}{7}\right)+\frac{5}{3}\cdot\frac{5}{3}\)
\(=-\frac{4}{21}+\frac{25}{6}=\frac{167}{42}\)
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