Math Problem Solver

\[ \frac{2}{7} + 2\frac{2}{3} - \frac{19}{8} = \frac{97}{168} = 0.577\overline{380952} \]

The sum can be computed by rewriting each term over a common denominator, where the least common denominator of \(\frac{2}{7}\), \(\frac{2}{1}\), \(\frac{2}{3}\), and \(\frac{-19}{8}\) is \(168\). \[ \begin{aligned} \frac{2}{7} + 2\frac{2}{3} - \frac{19}{8} &= \frac{2 \cdot 24}{7 \cdot 24} + \frac{2 \cdot 168}{1 \cdot 168} + \frac{2 \cdot 56}{3 \cdot 56} + \frac{-19 \cdot 21}{8 \cdot 21} \\ &= \frac{48 + 336 + 112 + -399}{168} \\ &= \frac{97}{168} \end{aligned} \]