\(\dfrac{x-1}{9}+\dfrac{x-2}{8}+\dfrac{x-3}{7}=3\)
\(\Leftrightarrow\left(\dfrac{x-1}{9}-1\right)+\left(\dfrac{x-2}{8}-1\right)+\left(\dfrac{x-3}{7}-1\right)=0\)
\(\Leftrightarrow\dfrac{x-10}{9}+\dfrac{x-10}{8}+\dfrac{x-10}{7}=0\)
\(\Leftrightarrow\left(x-10\right)\left(\dfrac{1}{9}+\dfrac{1}{8}+\dfrac{1}{7}\right)=0\)
\(\Leftrightarrow x-10=0\)
\(\Leftrightarrow x=10\)