Math Problem Solver

\[ \frac{-8}{21} + \frac{91}{3} + \frac{8}{54} = \frac{5689}{189} = 30.\overline{100529} \]

The sum can be computed by rewriting each term over a common denominator, where the least common denominator of \(\frac{-8}{21}\), \(\frac{91}{3}\), and \(\frac{8}{54}\) is \(378\). \[ \begin{aligned} \frac{-8}{21} + \frac{91}{3} + \frac{8}{54} &= \frac{-8 \cdot 18}{21 \cdot 18} + \frac{91 \cdot 126}{3 \cdot 126} + \frac{8 \cdot 7}{54 \cdot 7} \\ &= \frac{-144 + 11466 + 56}{378} \\ &= \frac{11378}{378} \\&= \frac{5689}{189} \end{aligned} \]