c) Để A>-1 thì A+1>0
\(\Leftrightarrow\dfrac{1-x}{x+1}+1>0\)
\(\Leftrightarrow\dfrac{1-x+x+1}{x+1}>0\)
\(\Leftrightarrow\dfrac{2}{x+1}>0\)
mà 2>0
nên x+1>0
hay x>-1
Kết hợp ĐKXĐ, ta được: \(\left\{{}\begin{matrix}x>-1\\x\ne1\end{matrix}\right.\)
a) Ta có: \(A=\left(\dfrac{x+1}{x-1}-\dfrac{1-x}{x+1}+\dfrac{4x^2}{1-x^2}\right):\dfrac{2x^2-2}{x^2-2x+1}\)
\(=\left(\dfrac{\left(x+1\right)^2}{\left(x-1\right)\left(x+1\right)}+\dfrac{\left(x-1\right)^2}{\left(x+1\right)\left(x-1\right)}-\dfrac{4x^2}{\left(x-1\right)\left(x+1\right)}\right):\dfrac{2\left(x^2-1\right)}{\left(x-1\right)^2}\)
\(=\dfrac{x^2+2x+1+x^2-2x+1-4x^2}{\left(x-1\right)\left(x+1\right)}:\dfrac{2\left(x-1\right)\left(x+1\right)}{\left(x-1\right)^2}\)
\(=\dfrac{-2x^2+2}{\left(x-1\right)\left(x+1\right)}\cdot\dfrac{\left(x-1\right)^2}{2\left(x-1\right)\left(x+1\right)}\)
\(=\dfrac{-2\left(x^2-1\right)}{\left(x-1\right)\left(x+1\right)}\cdot\dfrac{x-1}{2\left(x+1\right)}\)
\(=\dfrac{-2\cdot\left(x-1\right)}{2\left(x+1\right)}\)
\(=\dfrac{1-x}{x+1}\)
ĐKXĐ: \(x\notin\left\{1;-1\right\}\)
b) Để A=2 thì \(\dfrac{1-x}{x+1}=2\)
\(\Leftrightarrow1-x=2\left(x+1\right)\)
\(\Leftrightarrow1-x-2x-2=0\)
\(\Leftrightarrow-3x=1\)
hay \(x=-\dfrac{1}{3}\left(thỏa\right)\)
