\(\frac{14}{27}:\frac{7}{18}\cdot\frac{6}{5}+\frac{3}{10}\)
\(=\frac{14}{27}\cdot\frac{18}{7}\cdot\frac{6}{5}+\frac{3}{10}\)
\(=\frac{14\cdot18\cdot6}{27\cdot7\cdot5}+\frac{3}{10}\)
\(=\frac{2\cdot7\cdot9\cdot2\cdot3\cdot2}{3\cdot9\cdot7\cdot5}+\frac{3}{10}\)
\(=\frac{8}{5}+\frac{3}{10}\)
\(=\frac{16}{10}+\frac{3}{10}\)
\(=\frac{19}{10}\)