a: Ta có: \(P=\dfrac{2\sqrt{x}}{\sqrt{x}+3}+\dfrac{\sqrt{x}+1}{\sqrt{x}-3}+\dfrac{3-11\sqrt{x}}{9-x}\)
\(=\dfrac{2x-6\sqrt{x}+x+4\sqrt{x}+3-3+11\sqrt{x}}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}\)
\(=\dfrac{3x+9\sqrt{x}}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}\)
\(=\dfrac{3\sqrt{x}}{\sqrt{x}-3}\)
b: Thay \(x=\dfrac{7+4\sqrt{3}}{4}\) vào P, ta được:
\(P=\dfrac{3\cdot\dfrac{2+\sqrt{3}}{2}}{\dfrac{2+\sqrt{3}}{2}-3}=\dfrac{6+3\sqrt{3}}{2}:\dfrac{-4+\sqrt{3}}{2}=\dfrac{-33+18\sqrt{3}}{13}\)
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