To add \( \frac{9}{7} \) and \( \frac{5}{14} \), we need to find a common denominator. The least common multiple of 7 and 14 is 14.
First, we convert \( \frac{9}{7} \) to a fraction with a denominator of 14:
\[ \frac{9}{7} = \frac{9 \times 2}{7 \times 2} = \frac{18}{14} \]
Now we can add \( \frac{18}{14} \) and \( \frac{5}{14} \):
\[ \frac{18}{14} + \frac{5}{14} = \frac{18 + 5}{14} = \frac{23}{14} \]
Thus, \( \frac{9}{7} + \frac{5}{14} = \frac{23}{14} \).
This result can also be expressed as a mixed number:
\[ \frac{23}{14} = 1 \frac{9}{14} \]
So the final answer is:
\[ \frac{23}{14} \text{ or } 1 \frac{9}{14} \]