Math Problem Solver

\[ \frac{1}{13} + \frac{1}{78} - 39 = - \frac{3035}{78} = -38.9\overline{102564} \]

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 \(\frac{-39}{1}\) is \(78\). \[ \begin{aligned} \frac{1}{13} + \frac{1}{78} - 39 &= \frac{1 \cdot 6}{13 \cdot 6} + \frac{1 \cdot 1}{78 \cdot 1} + \frac{-39 \cdot 78}{1 \cdot 78} \\ &= \frac{6 + 1 + -3042}{78} \\ &= \frac{-3035}{78} \end{aligned} \]