\[\frac{17}{7} - \frac{8}{3} + \frac{10}{21} = \frac{17 \cdot 3}{7 \cdot 3} - \frac{8 \cdot 7}{3 \cdot 7} + \frac{10}{21} = \frac{51}{21} - \frac{56}{21} + \frac{10}{21}\]
\[\frac{51}{21} - \frac{56}{21} + \frac{10}{21} = \frac{51 - 56 + 10}{21} = \frac{-5 + 10}{21} = \frac{5}{21}\]
Ответ: \(\frac{5}{21}\)