Math Problem Solver

\[ 30 + \frac{-10}{19} = \frac{560}{19} = 29.\overline{473684210526315789} \]

The sum can be computed by rewriting each term over a common denominator, where the least common denominator of \(\frac{30}{1}\) and \(\frac{-10}{19}\) is \(19\). \[ \begin{aligned} 30 + \frac{-10}{19} &= \frac{30 \cdot 19}{1 \cdot 19} + \frac{-10 \cdot 1}{19 \cdot 1} \\ &= \frac{570 + -10}{19} \\ &= \frac{560}{19} \end{aligned} \]