Đáp án: x=-10
Giải thích các bước giải:
$\begin{array}{l}
\frac{{x + 1}}{9} + \frac{{x + 2}}{8} = \frac{{x + 3}}{7} + \frac{{x + 4}}{6}\\
\Rightarrow \frac{{x + 1}}{9} + 1 + \frac{{x + 2}}{8} + 1 = \frac{{x + 3}}{7} + 1 + \frac{{x + 4}}{6} + 1\\
\Rightarrow \frac{{x + 1 + 9}}{9} + \frac{{x + 2 + 8}}{8} = \frac{{x + 3 + 7}}{7} + \frac{{x + 4 + 6}}{6}\\
\Rightarrow \frac{{x + 10}}{9} + \frac{{x + 10}}{8} - \frac{{x + 10}}{7} - \frac{{x + 10}}{6} = 0\\
\Rightarrow \left( {x + 10} \right)\left( {\frac{1}{9} + \frac{1}{8} - \frac{1}{7} - \frac{1}{6}} \right) = 0\\
\Rightarrow x + 10 = 0\\
\Rightarrow x = - 10
\end{array}$
