\(a,P=\left(x-1\right)\left(1-\dfrac{1}{\sqrt{x}}\right):\dfrac{2\sqrt{x}-\sqrt{x}-1}{\sqrt{x}\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\\ P=\dfrac{\left(\sqrt{x}-1\right)^2\left(\sqrt{x}+1\right)}{\sqrt{x}}\cdot\dfrac{\sqrt{x}\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}{\sqrt{x}-1}\\ P=\left(\sqrt{x}-1\right)^2\left(\sqrt{x}+1\right)^2=\left(x-1\right)^2\)
\(b,P< 6-2\sqrt{5}\Leftrightarrow\left(x-1\right)^2< \left(\sqrt{5}-1\right)^2\\ \Leftrightarrow\left[{}\begin{matrix}x-1< \sqrt{5}-1\\x-1>1-\sqrt{5}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}0< x< \sqrt{5}\\x>2-\sqrt{5}\end{matrix}\right.\)
\(c,P< 9x^2\Leftrightarrow\left(x-1\right)^2< \left(3x\right)^2\\ \Leftrightarrow\left[{}\begin{matrix}x-1< 3x\\x-1>-3x\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x>-\dfrac{1}{2}\\x>\dfrac{1}{4}\end{matrix}\right.\)
