a,\(P=\left(\sqrt{x}-\dfrac{x+2}{\sqrt{x}+1}\right):\left(\dfrac{\sqrt{x}}{\sqrt{x}+1}-\dfrac{\sqrt{x}-4}{1-x}\right)\)
\(\Rightarrow P=\dfrac{\sqrt{x}\left(\sqrt{x}+1\right)-\left(x+2\right)}{\sqrt{x}+1}:\left(\dfrac{\sqrt{x}\left(\sqrt{x}-1\right)}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}+\dfrac{\sqrt{x}-4}{x-1}\right)\)
\(\Rightarrow P=\dfrac{x+\sqrt{x}-x-2}{\sqrt{x}+1}:\left(\dfrac{x-\sqrt{x}}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}+\dfrac{\sqrt{x}-4}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\right)\)
\(\Rightarrow P=\dfrac{\sqrt{x}-2}{\sqrt{x}+1}:\dfrac{x-\sqrt{x}+\sqrt{x}-4}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\)
\(\Rightarrow P=\dfrac{\sqrt{x}-2}{\sqrt{x}+1}:\dfrac{x-4}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\)
\(\Rightarrow P=\dfrac{\sqrt{x}-2}{\sqrt{x}+1}:\dfrac{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\)
\(\Rightarrow P=\dfrac{\sqrt{x}-2}{\sqrt{x}+1}.\dfrac{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\)
\(\Rightarrow P=\dfrac{\sqrt{x}-1}{\sqrt{x}+2}\)
b, Để P<0:
\(\Rightarrow\dfrac{\sqrt{x}-1}{\sqrt{x}+2}< 0\\ \Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}\sqrt{x}-1< 0\\\sqrt{x}+2>0\end{matrix}\right.\\\left\{{}\begin{matrix}\sqrt{x}-1>0\\\sqrt{x}+2< 0\end{matrix}\right.\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x< 1\\\sqrt{x}>-2\left(luôn.đúng\right)\end{matrix}\right.\\\left\{{}\begin{matrix}x>1\\\sqrt{x}< -2\left(sai\right)\end{matrix}\right.\end{matrix}\right.\)
\(\Rightarrow x< 1\)
Mà \(x\ge0\Rightarrow\left\{{}\begin{matrix}x\ge0\\x< 1\end{matrix}\right.\)
