\(P=\left(\dfrac{4\sqrt{x}}{\sqrt{x}+2}+\dfrac{8x}{4-x}\right):\left(\dfrac{\sqrt{x}-1}{x-2\sqrt{x}}-\dfrac{2}{\sqrt{x}}\right)\)
\(=\left(\dfrac{4\sqrt{x}\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}-\dfrac{8x}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\right):\left(\dfrac{\sqrt{x}-1}{\sqrt{x}\left(\sqrt{x}-2\right)}-\dfrac{2\left(\sqrt{x}-2\right)}{\sqrt{x}\left(\sqrt{x}-2\right)}\right)\)
\(=\left(\dfrac{4x-8\sqrt{x}-8x}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\right):\left(\dfrac{\sqrt{x}-1-2\sqrt{x}+4}{\sqrt{x}\left(\sqrt{x}-2\right)}\right)\)
\(=\dfrac{-\sqrt{x}\left(\sqrt{x}+2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}.\dfrac{\sqrt{x}\left(\sqrt{x}-2\right)}{3-\sqrt{x}}\)
\(=\dfrac{x}{\sqrt{x}-3}\)
\(P=-1\Rightarrow\dfrac{x}{\sqrt{x}-3}=-1\Rightarrow x=-\sqrt{x}+3\)
\(\Leftrightarrow x+\sqrt{x}-3=0\)
Đặt \(\sqrt{x}=t\ge0\Rightarrow t^2+t-3=0\Rightarrow\left[{}\begin{matrix}t=\dfrac{-1+\sqrt{13}}{2}\\t=\dfrac{-1-\sqrt{13}}{2}< 0\left(loại\right)\end{matrix}\right.\)
\(\Rightarrow\sqrt{x}=\dfrac{-1+\sqrt{13}}{2}\)
\(\Rightarrow x=\dfrac{7-\sqrt{13}}{2}\) (thỏa mãn)
