Ta có:
\(\dfrac{x-1}{x-2}-\dfrac{x-2}{x-3}=\dfrac{x-4}{x-5}-\dfrac{x-5}{x-6}\)
\(\Leftrightarrow\dfrac{\left(x-1\right)\left(x-3\right)-\left(x-2\right)^2}{\left(x-2\right)\left(x-3\right)}=\dfrac{\left(x-4\right)\left(x-6\right)-\left(x-5\right)^2}{\left(x-5\right)\left(x-6\right)}\)
\(\Leftrightarrow\dfrac{x^2-4x+3-x^2+4x-4}{x^2-5x+6}=\dfrac{x^2-10x+24-x^2+10x-25}{x^2-11x+30}\)
\(\Leftrightarrow\dfrac{-1}{x^2-5x+6}=\dfrac{-1}{x^2-11x+30}\)
\(\Leftrightarrow x^2-5x+6=x^2-11x+30\)
\(\Leftrightarrow-5x+11x=30-6\)
\(\Leftrightarrow6x=24\)
\(\Leftrightarrow x=4\)
Vậy \(S=\left\{4\right\}\)
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