\(\left(\dfrac{x+1}{2x-1}-1\right)\left(\dfrac{x-1}{x}+1\right)=1\left(đk:x\ne\dfrac{1}{2};x\ne0\right)\)
\(\Leftrightarrow\left(\dfrac{x+1}{2x-1}-\dfrac{2x-1}{2x-1}\right)\left(\dfrac{x-1}{x}+\dfrac{x}{x}\right)=1\)
\(\Leftrightarrow\dfrac{x+1-2x+1}{2x-1}\cdot\dfrac{x-1+x}{x}=1\)
\(\Leftrightarrow\dfrac{-x+2}{2x-1}\cdot\dfrac{2x-1}{x}=1\)
\(\Leftrightarrow\dfrac{-x+2}{x}=1\)
\(\Leftrightarrow-x+2=x\)
\(\Leftrightarrow2x=2\)
\(\Leftrightarrow x=1\left(tm\right)\)
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