Math Problem Solver

\[ \frac{5}{7} + \frac{2}{3} + \frac{19}{21} = \frac{16}{7} = 2.\overline{285714} \]

The sum can be computed by rewriting each term over a common denominator, where the least common denominator of \(\frac{5}{7}\), \(\frac{2}{3}\), and \(\frac{19}{21}\) is \(21\). \[ \begin{aligned} \frac{5}{7} + \frac{2}{3} + \frac{19}{21} &= \frac{5 \cdot 3}{7 \cdot 3} + \frac{2 \cdot 7}{3 \cdot 7} + \frac{19 \cdot 1}{21 \cdot 1} \\ &= \frac{15 + 14 + 19}{21} \\ &= \frac{48}{21} \\&= \frac{16}{7} \end{aligned} \]