\(đkxđ\Leftrightarrow x\ge0\)
\(\left(\sqrt{x}-\frac{1}{\sqrt{x}}\right):\left(\frac{\sqrt{x}-1}{\sqrt{x}}+\frac{1-\sqrt{x}}{x+\sqrt{x}}\right)\)
\(=\left(\frac{\sqrt{x}.\sqrt{x}-1}{\sqrt{x}}\right):\left(\frac{\sqrt{x}-1}{\sqrt{x}}-\frac{\sqrt{x}-1}{\sqrt{x}\left(\sqrt{x}+1\right)}\right)\)
\(=\left(\frac{x-1}{\sqrt{x}}\right):\left(\frac{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)-\sqrt{x}+1}{\sqrt{x}\left(\sqrt{x}+1\right)}\right)\)
\(=\frac{x-1}{\sqrt{x}}:\frac{x-1-\sqrt{x}+1}{\sqrt{x}\left(\sqrt{x}+1\right)}\)
\(=\frac{\left(x-1\right)\sqrt{x}\left(\sqrt{x}-1\right)}{\sqrt{x}.\sqrt{x}\left(\sqrt{x}-1\right)}=\frac{x-1}{\sqrt{x}}\)
\(b,P.\sqrt{x}=6\sqrt{x}-3-\sqrt{x}-4\)
\(\Rightarrow\frac{x-1}{\sqrt{x}}.\sqrt{x}=5\sqrt{x}-7\)
\(\Rightarrow x-5\sqrt{x}+6=0\)
\(\Rightarrow\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)=0\)
\(\Rightarrow\orbr{\begin{cases}\sqrt{x}=2\\\sqrt{x}=3\end{cases}\Rightarrow\orbr{\begin{cases}x=4\\x=9\end{cases}}}\)
Vậy \(x\in\left\{4;9\right\}\)
