*Rút gọn N
\(N=\dfrac{\sqrt{x}-1}{\sqrt{x}-3}-\dfrac{5\sqrt{x}-9}{\sqrt{x}\left(\sqrt{x}-3\right)}\)
\(N=\dfrac{x-\sqrt{x}-5\sqrt{x}+9}{\sqrt{x}\left(\sqrt{x}-3\right)}=\dfrac{x-6\sqrt{x}+9}{\sqrt{x}\left(\sqrt{x}-3\right)}\)
\(N=\dfrac{\left(\sqrt{x}-3\right)^2}{\sqrt{x}\left(\sqrt{x}-3\right)}=\dfrac{\sqrt{x}-3}{\sqrt{x}}\)
\(Q=M\cdot N=\dfrac{x-\sqrt{x}+3}{\sqrt{x}-3}\cdot\dfrac{\sqrt{x}-3}{\sqrt{x}}=\dfrac{x-\sqrt{x}+3}{\sqrt{x}}\)
Xét hiệu Q-2 ta có: \(Q-2=\dfrac{x-\sqrt{x}+3}{\sqrt{x}}-2=\dfrac{x-3\sqrt{x}+3}{\sqrt{x}}\)
\(=\dfrac{\left(\sqrt{x}-\dfrac{3}{2}\right)^2+\dfrac{3}{4}}{\sqrt{x}}>0\)
\(\Rightarrow Q-2>0\Rightarrow Q>2\)
