\(\dfrac{x-6}{7}+\dfrac{x-7}{8}+\dfrac{x-8}{9}=\dfrac{x-9}{10}+\dfrac{x-10}{11}+\dfrac{x-11}{12}\)
\(\Leftrightarrow\left(\dfrac{x-6}{7}+1\right)+\left(\dfrac{x-7}{8}+1\right)+\left(\dfrac{x-8}{9}+1\right)-\left(\dfrac{x-9}{10}+1\right)-\left(\dfrac{x-10}{11}+1\right)-\left(\dfrac{x-11}{12}+1\right)=0\)
\(\Leftrightarrow\dfrac{x+1}{7}+\dfrac{x+1}{8}+\dfrac{x+1}{9}-\dfrac{x+1}{10}-\dfrac{x+1}{11}-\dfrac{x+1}{12}=0\Leftrightarrow\left(x+1\right)\left(\dfrac{1}{7}+\dfrac{1}{8}+\dfrac{1}{9}-\dfrac{1}{10}-\dfrac{1}{11}-\dfrac{1}{12}\right)=0\Leftrightarrow x+1=0\Leftrightarrow x=-1\)(do \(\dfrac{1}{7}+\dfrac{1}{8}+\dfrac{1}{9}-\dfrac{1}{10}-\dfrac{1}{11}-\dfrac{1}{12}>0\))
b: Ta có: \(\dfrac{x-6}{7}+\dfrac{x-7}{8}+\dfrac{x-8}{9}=\dfrac{x-9}{10}+\dfrac{x-10}{11}+\dfrac{x-11}{12}\)
\(\Leftrightarrow\dfrac{x+1}{7}+\dfrac{x+1}{8}+\dfrac{x+1}{9}-\dfrac{x+1}{10}-\dfrac{x+1}{11}-\dfrac{x+1}{12}=0\)
\(\Leftrightarrow x+1=0\)
hay x=-1