a: \(P=\left(1-\sqrt{x}\right)\cdot\dfrac{\sqrt{x}-1+\sqrt{x}}{\sqrt{x}\left(1-\sqrt{x}\right)}\cdot\dfrac{x+\sqrt{x}-2\sqrt{x}+1}{2\sqrt{x}-1}\)
\(=\dfrac{2\sqrt{x}-1}{\sqrt{x}}\cdot\dfrac{x-\sqrt{x}+1}{2\sqrt{x}-1}=\dfrac{x-\sqrt{x}+1}{\sqrt{x}}\)
b: Để P>1 thì P-1>0
\(\Leftrightarrow\dfrac{x-3\sqrt{x}+1}{\sqrt{x}}>0\)
\(\Leftrightarrow\left(\sqrt{x}-\dfrac{3}{2}\right)^2-\dfrac{5}{4}>0\)
\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x}-\dfrac{3}{2}>\dfrac{5}{4}\\\sqrt{x}-\dfrac{3}{2}< -\dfrac{5}{4}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\sqrt{x}>\dfrac{11}{4}\\\sqrt{x}< \dfrac{1}{4}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\left[{}\begin{matrix}x>\dfrac{121}{16}\\x< -\dfrac{121}{16}\end{matrix}\right.\\0< x< \dfrac{1}{16}\end{matrix}\right.\)
