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