We want to find $ \frac{1}{2} + \frac{2}{7} - \frac{5}{8} $. The common denominator is 56, so we try to rewrite each of the three fractions with 56 on the bottom. $ \frac{1}{2} = \frac{1}{2} \cdot \frac{28}{28} = \frac{28}{56} $. Also, $ \frac{2}{7} = \frac{2}{7} \cdot \frac{8}{8} = \frac{16}{56} $. Finally, $ \frac{5}{8} = \frac{5}{8} \cdot \frac{7}{7} = \frac{35}{56} $. Thus, we have $ \frac{1}{2} + \frac{2}{7} - \frac{5}{8} = \frac{28}{56} + \frac{16}{56} - \frac{35}{56} = \frac{28+16-35}{56} = \frac{44-35}{56} = \frac{9}{56} $. Because 9 and 56 have no common divisors, this is the simplest form, and our answer is $ \boxed{\frac{9}{56}} $.