\(A=\left(\dfrac{1+x}{1-x}-\dfrac{1-x}{1+x}+\dfrac{4x^2}{1-x^2}\right):\dfrac{4x^2-4}{x^2-2x+1}\)
\(\Leftrightarrow A=\dfrac{\left(1+x\right)^2-\left(1-x\right)^2+4x^2}{\left(1-x\right)\left(1+x\right)}:\dfrac{4\left(x-1\right)\left(x+1\right)}{\left(x-1\right)^2}\)
\(\Leftrightarrow A=\dfrac{1+2x+x^2-1+2x-x^2+4x^2}{\left(1-x\right)\left(1+x\right)}:\dfrac{4\left(x+1\right)}{x-1}\)
\(\Leftrightarrow A=\dfrac{4x^2+4x}{\left(1-x\right)\left(1+x\right)}.\dfrac{x-1}{4\left(x+1\right)}\)
\(\Leftrightarrow A=\dfrac{-4x\left(x+1\right)}{\left(x-1\right)\left(1+x\right)}.\dfrac{x-1}{4\left(x+1\right)}\)
\(\Leftrightarrow A=\dfrac{-x}{1+x}\)
\(ĐKXĐ:\left\{{}\begin{matrix}1-x\ne0\\1+x\ne0\\1-x^2\ne0\\x^2-2x+1\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ne1\\x\ne-1\\x\ne\pm1\\\left(x-1\right)^2\ne0\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x\ne\pm1\\x\ne1\end{matrix}\right.\Leftrightarrow x\ne\pm1\)
