a, Để A xác định
\(\Leftrightarrow\left\{{}\begin{matrix}2x-2\ne0\\x^2-1\ne0\\2x+2\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ne1\\x\ne-1\end{matrix}\right.\)
\(b,A=\dfrac{x+1}{2x-2}+\dfrac{2x}{x^2-1}-\dfrac{x+3}{2x+2}\)
\(=\dfrac{x+1}{2\left(x-1\right)}+\dfrac{2x}{\left(x-1\right)\left(x+1\right)}-\dfrac{x+3}{2\left(x+1\right)}\)
\(=\dfrac{\left(x+1\right)^2}{2\left(x-1\right)\left(x+1\right)}+\dfrac{2x.2}{2\left(x-1\right)\left(x+1\right)}-\dfrac{\left(x+3\right)\left(x-1\right)}{2\left(x+1\right)\left(x-1\right)}\)
\(=\dfrac{x^2+2x+1+4x-x^2+2x-3}{2\left(x-1\right)\left(x+1\right)}\)
\(=\dfrac{8x-2}{2\left(x-1\right)\left(x+1\right)}\)
\(=\dfrac{2\left(4x-1\right)}{2\left(x-1\right)\left(x+1\right)}=\dfrac{4x-1}{x^2-1}\)
