\(ĐKXĐ:x\ne0,x\ne1\)
\(\dfrac{x-2}{x}+\dfrac{x}{x-1}=\dfrac{11}{6}\)
\(\Leftrightarrow6\left(x-1\right)\left(x-2\right)+6x^2=11x\left(x-1\right)\)
\(\Leftrightarrow6\left(x-1\right)\left(x-2\right)-11x\left(x-1\right)+6x^2=0\)
\(\Leftrightarrow\left(x-1\right)\left[6\left(x-2\right)-11x\right]+6x=0\)
\(\Leftrightarrow\left(x-1\right)\left(6x-12-11x\right)+6x=0\)
\(\Leftrightarrow\left(x-1\right)\left(-5x-12\right)+6x=0\)
\(\Leftrightarrow-5x^2-12x+5x+12+6x=0\)
\(\Leftrightarrow x^2-7x+12=0\)
\(\Leftrightarrow\left(x-4\right)\left(x-3\right)=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}x-4=0\\x-3=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=4\left(tm\right)\\x=3\left(tm\right)\end{matrix}\right.\)
