$\frac{x+1}{9}+\frac{x+2}{8}=\frac{x+3}{7}+\frac{x+4}{6}$
$\Leftrightarrow \frac{x+1}{9}+1+\frac{x+2}{8}+1=\frac{x+3}{7}+1+\frac{x+4}{6}$
$\Leftrightarrow \frac{x+10}{9}+\frac{x+10}{8}=\frac{x+10}{7}+\frac{x+10}{6}$
$\Leftrightarrow \frac{x+10}{9}+\frac{x+10}{8}-\frac{x+10}{7}-\frac{x+10}{6}=0$
$\Leftrightarrow (x+10)(\frac{1}{9}+\frac{1}{8}-\frac{1}{7}-\frac{1}{6})=0$
Vì $\frac{1}{9}+\frac{1}{8}-\frac{1}{7}-\frac{1}{6}\ne0$
$\Rightarrow x+10=0$
$\Leftrightarrow x=-10$
Vậy $x=-10$
