Giải phương trình sau: x- 2/7 + x-1 /8 = x- 4/5 + x-3/6

Ta có: \(\frac{{x - 2}}{7} + \frac{{x - 1}}{8} = \frac{{x - 4}}{5} + \frac{{x - 3}}{6}\)

\(\frac{{x - 2}}{7} - 1 + \frac{{x - 1}}{8} - 1 = \frac{{x - 4}}{5} - 1 + \frac{{x - 3}}{6} - 1\)

\(\frac{{x - 9}}{7} + \frac{{x - 9}}{8} = \frac{{x - 9}}{5} + \frac{{x - 9}}{6}\)

\(\frac{{x - 9}}{7} + \frac{{x - 9}}{8} - \frac{{x - 9}}{5} - \frac{{x - 9}}{6} = 0\)

\(\left( {x - 9} \right)\left( {\frac{1}{7} + \frac{1}{8} - \frac{1}{5} - \frac{1}{6}} \right) = 0\)

Nhận thấy \(\left( {\frac{1}{7} + \frac{1}{8} - \frac{1}{5} - \frac{1}{6}} \right) \ne 0\) nên \(x - 9 = 0\) hay \(x = 9\).

Vậy \(x = 9.\)