ĐKXĐ : \(\left\{{}\begin{matrix}2x+1\ne0\\2x-1+\frac{2-4x}{2x+1}\ne0\end{matrix}\right.\) => \(x\ne\pm\frac{1}{2}\)
Ta có : \(\frac{\frac{2x-1}{2x+1}}{2x-1+\frac{2-4x}{2x+1}}=\left(\frac{2x-1}{2x+1}\right)\left(\frac{2x+1}{\left(2-4x\right)+\left(2x-1\right)\left(2x+1\right)}\right)\)
\(=\frac{\left(2x+1\right)\left(2x-1\right)}{\left(\left(2-4x\right)+\left(2x-1\right)\left(2x+1\right)\right)\left(2x+1\right)}\)
\(=\frac{2x-1}{\left(2-4x\right)+\left(2x-1\right)\left(2x+1\right)}=\frac{2x-1}{\left(2x-1\right)^2}=\frac{1}{2x-1}\)
