a: Khi x=9 thì \(M=\dfrac{3-1}{3}=\dfrac{2}{3}\)
b: \(P=\dfrac{\left(\sqrt{x}-2\right)\left(\sqrt{x}-1\right)+8\sqrt{x}+2}{x-1}+\dfrac{2}{\sqrt{x}-1}\)
\(=\dfrac{x-3\sqrt{x}+2+8\sqrt{x}+2}{x-1}+\dfrac{2\sqrt{x}+2}{x-1}\)
\(=\dfrac{x+5\sqrt{x}+4+2\sqrt{x}+2}{\left(x-1\right)}=\dfrac{x+7\sqrt{x}+6}{x-1}\)
\(=\dfrac{\sqrt{x}+6}{\sqrt{x}-1}\)
c: \(Q=M\cdot P+\dfrac{x-5}{\sqrt{x}}\)
\(=\dfrac{\sqrt{x}+6}{\sqrt{x}-1}\cdot\dfrac{\sqrt{x}-1}{\sqrt{x}}+\dfrac{x-5}{\sqrt{x}}\)
\(=\dfrac{x-5+\sqrt{x}+6}{\sqrt{x}}=\dfrac{x+\sqrt{x}+1}{\sqrt{x}}\)
\(Q-3=\dfrac{x+\sqrt{x}+1-3\sqrt{x}}{\sqrt{x}}=\dfrac{x-2\sqrt{x}+1}{\sqrt{x}}\)
\(=\dfrac{\left(\sqrt{x}-1\right)^2}{\sqrt{x}}>0\)
=>Q>3
