a: \(K=\left(1-\dfrac{\sqrt{x}}{x-9}+\dfrac{3}{\sqrt{x}-3}\right):\dfrac{\sqrt{x}}{\sqrt{x}+3}\)
\(=\dfrac{x-9-\sqrt{x}+3\left(\sqrt{x}+3\right)}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}\cdot\dfrac{\sqrt{x}+3}{\sqrt{x}}\)
\(=\dfrac{x-\sqrt{x}-9+3\sqrt{x}+9}{\sqrt{x}\left(\sqrt{x}-3\right)}=\dfrac{x+2\sqrt{x}}{\sqrt{x}\left(\sqrt{x}-3\right)}\)
\(=\dfrac{\sqrt{x}+2}{\sqrt{x}-3}\)
b: Thay \(x=11+6\sqrt{2}=\left(3+\sqrt{2}\right)^2\) vào K, ta được:
\(K=\dfrac{\sqrt{\left(3+\sqrt{2}\right)^2}+2}{\sqrt{\left(3+\sqrt{2}\right)^2}-3}=\dfrac{3+\sqrt{2}+2}{3+\sqrt{2}-3}=\dfrac{5+\sqrt{2}}{\sqrt{2}}=\dfrac{5\sqrt{2}+2}{2}\)
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