\(\dfrac{2x-1}{3}+\dfrac{x-2}{x}=1\)
\(\Rightarrow\dfrac{x\left(2x-1\right)+3\left(x-2\right)}{3x}=1\)
\(\Rightarrow2x^2-x+3x-6=3x\)
\(\Rightarrow2x^2-x+3x-6-3x=0\)
\(\Rightarrow2x^2-x-6=0\)
\(\Rightarrow2x^2-4x+3x-6=0\)
\(\Rightarrow2x.\left(x-2\right)+3.\left(x-2\right)=0\)
\(\Rightarrow\left(x-2\right)\left(2x+3\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-2=0\\2x+3=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=2\\x=-\dfrac{3}{2}\end{matrix}\right.\)
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\(\dfrac{2x-1}{3}+\dfrac{x-2}{x}=1\) (1)
ĐKXĐ: \(x\ne0\)
\(\left(1\right)\Leftrightarrow\dfrac{x\left(2x-1\right)}{3x}+\dfrac{3\left(x-2\right)}{3x}-\dfrac{3x}{3x}=0\)
\(\Leftrightarrow\dfrac{2x^2-x+3x-6-3x}{3x}=0\)
\(\Rightarrow2x^2-x-6=0\)
\(\Leftrightarrow2x^2-4x+3x-6=0\)
\(\Leftrightarrow2x\left(x-2\right)+3\left(x-2\right)=0\)
\(\Leftrightarrow\left(2x+3\right)\left(x-2\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}2x+3=0\\x-2=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}2x=-3\\x=2\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-\dfrac{3}{2}\\x=2\end{matrix}\right.\)
\(\dfrac{2x-1}{3}+\dfrac{x-2}{x}=1\:\left(ĐKXĐ:\:x\ne0\right)\\ \Rightarrow2x^2-x+3x-6=3x\\ 2x^2-x-6=0\\ 2x^2+3x-4x-6=0\\ \left(2x+3\right)\left(x-2\right)=0\\ \Rightarrow\left[{}\begin{matrix}2x+3=0\\x-2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{3}{2}\\x=2\end{matrix}\right.\)
