a: Khi x=9 thì \(B=\dfrac{4\left(3+2\right)}{3-2}=4\cdot5=20\)
b: \(A=\dfrac{\sqrt{x}+2}{\sqrt{x}-2}-\dfrac{\sqrt{x}-2}{\sqrt{x}+2}-\dfrac{4x}{4-x}\)
\(=\dfrac{\sqrt{x}+2}{\sqrt{x}-2}-\dfrac{\sqrt{x}-2}{\sqrt{x}+2}+\dfrac{4x}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)
\(=\dfrac{x+4\sqrt{x}+4-\left(x-4\sqrt{x}+4\right)+4x}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)
\(=\dfrac{5x+4\sqrt{x}+4-x+4\sqrt{x}-4}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)
\(=\dfrac{4x+8\sqrt{x}}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}=\dfrac{4\sqrt{x}}{\sqrt{x}-2}\)
c: \(M=A:B=\dfrac{4\sqrt{x}}{\sqrt{x}-2}:\dfrac{4\left(\sqrt{x}+2\right)}{\sqrt{x}-2}\)
\(=\dfrac{4\sqrt{x}}{\sqrt{x}-2}\cdot\dfrac{\sqrt{x}-2}{4\left(\sqrt{x}+2\right)}=\dfrac{\sqrt{x}}{\sqrt{x}+2}\)
\(M=\dfrac{\sqrt{x}}{\sqrt{x}+2}=\dfrac{\sqrt{x}+2-2}{\sqrt{x}+2}=1-\dfrac{2}{\sqrt{x}+2}\)
=>\(0< =M< 1\)
=>\(M>=\sqrt{M}\)
