Điều kiện: \(\left\{{}\begin{matrix}x^2-2x+1\ne0\\x^2-1\ne0\\x^2+2x+1\ne0\\5x^2+5\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\left(x-1\right)^2\ne0\\\left(x-1\right)\left(x+1\right)\ne0\\\left(x+1\right)^2\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ne1\\x\ne-1\end{matrix}\right.\)
\(E=\left(\dfrac{3x+2}{x^2-2x+1}-\dfrac{6}{x^2-1}-\dfrac{3x-2}{x^2+2x+1}\right).\dfrac{x^2+2x+1}{5x^2+5}\)
\(=\left[\dfrac{3x+2}{\left(x-1\right)^2}-\dfrac{6}{\left(x-1\right)\left(x+1\right)}-\dfrac{3x-2}{\left(x+1\right)^2}\right].\dfrac{\left(x+1\right)^2}{5x^2+5}\)
\(=\dfrac{\left(3x+2\right)\left(x+1\right)^2-6\left(x-1\right)\left(x+1\right)-\left(3x-2\right)\left(x-1\right)^2}{\left(x-1\right)^2.\left(x+1\right)^2}.\dfrac{\left(x+1\right)^2}{5x^2+5}\)
\(=\dfrac{\left(3x+2\right)\left(x^2+2x+1\right)-6\left(x^2-1\right)-\left(3x-2\right)\left(x^2-2x+1\right)}{\left(x-1\right)^2.\left(x+1\right)^2}.\dfrac{\left(x+1\right)^2}{5x^2+5}\)
\(=\dfrac{\left(3x^3+6x^2+3x+2x^2+4x+2\right)-\left(6x^2-6\right)-\left(3x^3-6x^2+3x-2x^2+4x-2\right)}{\left(x-1\right)^2.\left(x+1\right)^2}.\dfrac{\left(x+1\right)^2}{5x^2+5}\)
\(=\dfrac{3x^3+8x^2+7x+2-6x^2+6-3x^3+8x^2-7x+2}{\left(x-1\right)^2.\left(x+1\right)^2}.\dfrac{\left(x+1\right)^2}{5x^2+5}\)
\(=\dfrac{10x^2+10}{\left(x-1\right)^2.\left(x+1\right)^2}.\dfrac{\left(x+1\right)^2}{5x^2+5}\)
\(=\dfrac{10\left(x^2+1\right)}{\left(x-1\right)^2.\left(x+1\right)^2}.\dfrac{\left(x+1\right)^2}{5\left(x^2+1\right)}\)
\(=\dfrac{2}{\left(x-1\right)^2}\)
