giải phương trình sau : x-1 / 9 + x-2/ 8 + x-3/ 7 = x-4/ 6 + x-5 / 5+ x-6 /4

Ta có: \(\frac{{x - 1}}{9} + \frac{{x - 2}}{8} + \frac{{x - 3}}{7} = \frac{{x - 4}}{6} + \frac{{x - 5}}{5} + \frac{{x - 6}}{4}\)

\(\frac{{x - 1}}{9} - 1 + \frac{{x - 2}}{8} - 1 + \frac{{x - 3}}{7} - 1 = \frac{{x - 4}}{6} - 1 + \frac{{x - 5}}{5} - 1 + \frac{{x - 6}}{4} - 1\)

\(\frac{{x - 10}}{9} + \frac{{x - 10}}{8} + \frac{{x - 10}}{7} = \frac{{x - 10}}{6} + \frac{{x - 10}}{5} + \frac{{x - 10}}{4}\)

\(\frac{{x - 10}}{9} + \frac{{x - 10}}{8} + \frac{{x - 10}}{7} - \frac{{x - 10}}{6} - \frac{{x - 10}}{5} - \frac{{x - 10}}{4} = 0\)

\(\left( {x - 10} \right)\left( {\frac{1}{9} + \frac{1}{8} + \frac{1}{7} - \frac{1}{6} - \frac{1}{5} - \frac{1}{4}} \right) = 0\)

Nhận thấy \(\left( {\frac{1}{9} + \frac{1}{8} + \frac{1}{7} - \frac{1}{6} - \frac{1}{5} - \frac{1}{4}} \right) \ne 0\) nên \(x - 10 = 0\) suy ra \(x = 10.\)

Vậy \(x = 10.\)