\[\frac{6}{7} \cdot \frac{7}{6} \cdot \frac{8}{9} \cdot \frac{9}{8} \cdot \frac{10}{11} \cdot \frac{11}{10} \cdot \frac{12}{13} \cdot \frac{13}{12} \cdot \frac{14}{19} = \frac{14}{19}.\]