$\begin{array}{l}P = \dfrac{2\sqrt x -9}{x -5\sqrt x + 6}-\dfrac{\sqrt x + 3}{\sqrt x -2}- \dfrac{2\sqrt x +1}{3 - \sqrt x}\\ ĐKXĐ: \, x \geq 0;\, x \ne 4;\, x \ne 9\\ a)\,\,P = \dfrac{2\sqrt x -9}{(\sqrt x -2)(\sqrt x -3)} - \dfrac{(\sqrt x +3)(\sqrt x - 3)}{(\sqrt x -2)(\sqrt x -3)}+ \dfrac{(2\sqrt x +1)(\sqrt x - 2)}{(\sqrt x -2)(\sqrt x -3)}\\ = \dfrac{2\sqrt x - 9 -(x - 9) + (2x - 4\sqrt x + \sqrt x -2)}{(\sqrt x -2)(\sqrt x -3)}\\ =\dfrac{x - \sqrt 2 - 2}{(\sqrt x -2)(\sqrt x -3)}\\ = \dfrac{(\sqrt x + 1)(\sqrt x -2)}{(\sqrt x -2)(\sqrt x -3)}\\ =\dfrac{\sqrt x +1}{\sqrt x - 3}\\ b)\,\,P < 1\\ \Leftrightarrow \dfrac{\sqrt x +1}{\sqrt x - 3} < 1\\ \Leftrightarrow \sqrt x + 1 < \sqrt x - 3\\ \Leftrightarrow 1 < -3 \,\,\,\,\,\,\,\,(\text{vô lí)}\\ \text{Vậy không có giá trị x thỏa mãn P < 1}\\ c)\,\,\dfrac{1}{P} = \dfrac{\sqrt x - 3}{\sqrt x + 1}=1 - \dfrac{4}{\sqrt x + 1}\\ \text{Ta có:}\\ \sqrt x \geq 0\\ \Leftrightarrow \sqrt x + 1 \geq 1\\ \Leftrightarrow \dfrac{1}{\sqrt x + 1} \leq 1\\ \Leftrightarrow \dfrac{-4}{\sqrt x + 1} \geq -4\\ \Leftrightarrow 1 - \dfrac{4}{\sqrt x +1} \geq -3\\ Hay\,\,\,\dfrac{1}{P} \geq -3\\ \text{Dấu = xảy ra}\,\,\Leftrightarrow \sqrt x = 0 \Leftrightarrow x = 0\\ Vậy \,\,\,min\dfrac{1}{P} = - 3 \Leftrightarrow x = 0\end{array}$
