Math Problem Solver

\[ \frac{1}{13} + \frac{1}{78} - \frac{1}{39} = \frac{5}{78} = 0.0\overline{641025} \]

The sum can be computed by rewriting each term over a common denominator, where the least common denominator of \(\frac{1}{13}\), \(\frac{1}{78}\), and \(\frac{-1}{39}\) is \(78\). \[ \begin{aligned} \frac{1}{13} + \frac{1}{78} - \frac{1}{39} &= \frac{1 \cdot 6}{13 \cdot 6} + \frac{1 \cdot 1}{78 \cdot 1} + \frac{-1 \cdot 2}{39 \cdot 2} \\ &= \frac{6 + 1 + -2}{78} \\ &= \frac{5}{78} \end{aligned} \]