\(\Leftrightarrow\dfrac{x+1}{9}+1+\dfrac{x+2}{8}+1=\dfrac{x+3}{7}+1+\dfrac{x+4}{6}+1\)
=>x+10=0
hay x=-10
\(\Leftrightarrow\dfrac{x+1}{9}+1+\dfrac{x+2}{8}+1=\dfrac{x+3}{7}+1+\dfrac{x+4}{6}+1\)
\(\Leftrightarrow\dfrac{x+10}{9}+\dfrac{x+10}{8}-\dfrac{x+10}{7}-\dfrac{x+10}{6}=0\Leftrightarrow x+10=0\Leftrightarrow x=-10\)
\(\dfrac{x+1}{9}+\dfrac{x+2}{8}=\dfrac{x+3}{7}+\dfrac{x+4}{6}\)
\(\left(\dfrac{x+1}{9}+1\right)+\left(\dfrac{x+2}{8}+1\right)-\left(\dfrac{x+3}{7}+1\right)-\left(\dfrac{x+4}{6}+1\right)=0\)
\(\dfrac{x+10}{9}+\dfrac{x+10}{8}-\dfrac{x+10}{7}-\dfrac{x+10}{6}=0\)
\(\left(x+10\right)\left(\dfrac{1}{9}+\dfrac{1}{8}-\dfrac{1}{7}-\dfrac{1}{6}\right)=0\)
\(x+10=0\)
\(x=-10\)
\(PT\Leftrightarrow\dfrac{x+1}{9}+1+\dfrac{x+2}{8}+1-\dfrac{x+3}{7}+1-\dfrac{x+4}{6}+1=0\)
\(\Leftrightarrow\left(x+10\right)\left(\dfrac{1}{9}+\dfrac{1}{8}-\dfrac{1}{7}-\dfrac{1}{6}=0\right)\)
Mà \(\dfrac{1}{9}+\dfrac{1}{8}-\dfrac{1}{7}-\dfrac{1}{6}< 0\)
\(\Rightarrow x+10=0\)
\(\Leftrightarrow x=-10\)
Vậy: \(S=\left\{-10\right\}\)