a) ĐKXĐ:
\(\left\{{}\begin{matrix}x\ge0\\\sqrt{x}-1\ne0\\x-1\ne0\\\sqrt{x}+1\ne0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ge0\\\sqrt{x}\ne1\\x\ne1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ge0\\x\ne1\end{matrix}\right.\)
b) A = \(\left(\frac{1}{\sqrt{x}-1}-\frac{\sqrt{x}}{x-1}\right):\frac{1}{\sqrt{x}+1}\)
= \(\frac{\sqrt{x}+1-\sqrt{x}}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}.\left(\sqrt{x}+1\right)\)
=\(\frac{\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)
= \(\frac{1}{\sqrt{x}-1}\)
c) A = \(\frac{-1}{2}\)
\(\Leftrightarrow\frac{1}{\sqrt{x}-1}=\frac{-1}{2}\)
\(\Leftrightarrow\sqrt{x}-1=-2\)
\(\Leftrightarrow\sqrt{x}=-1\) (vô lý)
Vậy không tồn tại x để A = \(\frac{-1}{2}\)
