Math Problem Solver

\[ 6 - \frac{3}{5} - \frac{4}{7} + \frac{2}{9} = \frac{1591}{315} = 5.0\overline{507936} \]

The sum can be computed by rewriting each term over a common denominator, where the least common denominator of \(\frac{6}{1}\), \(\frac{-3}{5}\), \(\frac{-4}{7}\), and \(\frac{2}{9}\) is \(315\). \[ \begin{aligned} 6 - \frac{3}{5} - \frac{4}{7} + \frac{2}{9} &= \frac{6 \cdot 315}{1 \cdot 315} + \frac{-3 \cdot 63}{5 \cdot 63} + \frac{-4 \cdot 45}{7 \cdot 45} + \frac{2 \cdot 35}{9 \cdot 35} \\ &= \frac{1890 + -189 + -180 + 70}{315} \\ &= \frac{1591}{315} \end{aligned} \]