đk : x khác -9 ; -10
\(\dfrac{x+9}{10}+1+\dfrac{x+10}{9}+1=\dfrac{9}{x+10}+1+\dfrac{10}{x+9}+1\)
\(\Leftrightarrow\dfrac{x+19}{10}+\dfrac{x+19}{9}=\dfrac{x+19}{x+10}+\dfrac{x+19}{x+9}\)
\(\Leftrightarrow\left(x+19\right)\left(\dfrac{1}{10}+\dfrac{1}{9}-\dfrac{1}{x+10}-\dfrac{1}{x+9}\right)=0\Leftrightarrow x=-19\)