\(A=\left(\dfrac{2\sqrt{x}\left(\sqrt{x}-3\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}+\dfrac{\sqrt{x}\left(\sqrt{x}+3\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}-\dfrac{3\left(\sqrt{x}+3\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\right):\left(\dfrac{2\sqrt{x}-2}{\sqrt{x}-3}-\dfrac{\sqrt{x}-3}{\sqrt{x}-3}\right)\)
\(=\left(\dfrac{3x-6\sqrt{x}-9}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\right):\left(\dfrac{\sqrt{x}+1}{\sqrt{x}-3}\right)\)
\(=\dfrac{3\left(\sqrt{x}+1\right)\left(\sqrt{x}-3\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}.\dfrac{\left(\sqrt{x}-3\right)}{\left(\sqrt{x}+1\right)}\)
\(=\dfrac{3\left(\sqrt{x}-3\right)}{\sqrt{x}+3}\)
Để \(A< -1\Rightarrow\dfrac{3\left(\sqrt{x}-3\right)}{\sqrt{x}+3}< -1\)
\(\Rightarrow3\sqrt{x}-9< -\sqrt{x}-3\)
\(\Rightarrow4\sqrt{x}< 6\)
\(\Rightarrow\sqrt{x}< \dfrac{3}{2}\Rightarrow x< \dfrac{9}{4}\)
kết hợp ĐKXĐ \(\Rightarrow0\le x< \dfrac{9}{4}\)
