Ответ:

\[\frac{24}{49}:\frac{6}{7}+\frac{1}{14}=\frac{24}{49}\cdot\frac{7}{6}+\frac{1}{14}=\frac{4}{7}+\frac{1}{14}=\frac{8}{14}+\frac{1}{14}=\frac{9}{14}.\]

Ответ: \(\frac{9}{14}\).