a. \(\left[{}\begin{matrix}\left\{{}\begin{matrix}x+1>0\\x-1>0\end{matrix}\right.\\\left\{{}\begin{matrix}x+1< 0\\x-1< 0\end{matrix}\right.\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>-1\\x>1\end{matrix}\right.\\\left\{{}\begin{matrix}x< -1\\x< 1\end{matrix}\right.\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x>1\\x< -1\end{matrix}\right.\)
b. \(\dfrac{x^2+x-2}{x-9}=\dfrac{\left(x-1\right)\left(x+2\right)}{x-9}\) (với \(x\ne9\) )
\(\left[{}\begin{matrix}\left\{{}\begin{matrix}x-1< 0\\x+2>0\\x-9>0\end{matrix}\right.\\\left\{{}\begin{matrix}x-1>0\\x+2< 0\\x-9>0\end{matrix}\right.\\\left\{{}\begin{matrix}x-1>0\\x+2>0\\x-9< 0\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\) \(\left[{}\begin{matrix}\left\{{}\begin{matrix}x< 1\\x>-2\\x>9\end{matrix}\right.\\\left\{{}\begin{matrix}x>1\\x< -2\\x>9\end{matrix}\right.\\\left\{{}\begin{matrix}x>1\\x>-2\\x< 9\end{matrix}\right.\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x< -2\\1< x< 9\end{matrix}\right.\)
