\(\frac{4}{7}+\frac{2}{5}\cdot(\frac{1}{5}+\frac{1}{10})=\frac{4}{7}+\frac{2}{5}\cdot(\frac{2}{10}+\frac{1}{10})=\frac{4}{7}+\frac{2}{5}\cdot\frac{3}{10}=\frac{4}{7}+\frac{1}{5}\cdot\frac{3}{5}\\\\=\frac{4}{7}+\frac{6}{25}=\frac{4\cdot25}{7\cdot25}+\frac{6\cdot7}{25\cdot7}=\frac{100}{175}+\frac{42}{175}=\frac{142}{175}\)
