a) \(P=\sqrt{12}-\dfrac{3}{\sqrt{3}}-\dfrac{2}{\sqrt{3}+1}\)
\(P=\sqrt{2^2\cdot3}-\sqrt{3}-\dfrac{2\left(\sqrt{3}-1\right)}{\left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right)}\)
\(P=2\sqrt{3}-\sqrt{3}-\dfrac{2\left(\sqrt{3}-1\right)}{3-1}\)
\(P=\sqrt{3}-\dfrac{2\left(\sqrt{3}-1\right)}{2}\)
\(P=\sqrt{3}-\sqrt{3}+1\)
\(P=1\)
\(Q=\left(\dfrac{\sqrt{x}}{x-9}-\dfrac{2}{3-\sqrt{x}}\right):\dfrac{3}{\sqrt{x}+3}\)
\(Q=\left[\dfrac{\sqrt{x}}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}+\dfrac{2}{\sqrt{x}-3}\right]:\dfrac{3}{\sqrt{x}+3}\)
\(Q=\left[\dfrac{\sqrt{x}}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}+\dfrac{2\left(\sqrt{x}+3\right)}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}\right]\cdot\dfrac{\sqrt{x}+3}{3}\)
\(Q=\dfrac{\sqrt{x}+2\sqrt{x}+3}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}\cdot\dfrac{\sqrt{x}+3}{3}\)
\(Q=\dfrac{3\sqrt{x}+3}{3\left(\sqrt{x}-3\right)}\)
\(Q=\dfrac{3\left(\sqrt{x}+1\right)}{3\left(\sqrt{x}-3\right)}\)
\(Q=\dfrac{\sqrt{x}+1}{\sqrt{x}-3}\)
b) Ta có: \(Q-P\)
\(=\dfrac{\sqrt{x}+1}{\sqrt{x}-3}-1=\dfrac{\sqrt{x}+1-\left(\sqrt{x}-3\right)}{\sqrt{x}-3}=\dfrac{4}{\sqrt{x}-3}\)
Biểu thức không âm khi: \(\dfrac{4}{\sqrt{x}-3}>0\)
\(\Leftrightarrow\sqrt{x}-3>0\)
\(\Leftrightarrow\sqrt{x}>3\)
\(\Leftrightarrow x>9\)
