`(a):\ P=(1)/(\sqrt{x})-(\sqrt{x})/(\sqrt{x}+3)+(4x-3\sqrt{x}-3)/(\sqrt{x}(\sqrt{x}+3))\ (x>0)`
`=(\sqrt{x}+3-\sqrt{x}^{2}+4x-3\sqrt{x}-3)/(\sqrt{x}(\sqrt{x}+3))`
`=(\sqrt{x}+3-x+4x-3\sqrt{x}-3)/(\sqrt{x}(\sqrt{x}+3))`
`=(3x-2\sqrt{x})/(\sqrt{x}(\sqrt{x}+3))`
`=(3\sqrt{x}-2)/(\sqrt{x}+3)\ (DPCM)`
`(b):\ x=20-6\sqrt{11}=9-2.3.\sqrt{11}+11`
`=(3-\sqrt{11})^{2}`
`=>\sqrt{x}=\sqrt{(3-\sqrt{11})^{2}}=|3-\sqrt{11}|=\sqrt{11}-3`
Thay `\sqrt{x}=\sqrt{11}-3\ (TMDK)` vào `P`, ta được :
`P=(3.(\sqrt{11}-3)-2)/(\sqrt{11}-3+3)=(3\sqrt{11}-11)/(\sqrt{11})`
`=(\sqrt{11}(3-\sqrt{11}))/(\sqrt{11})=3-\sqrt{11}`
a: \(=\dfrac{\sqrt{x}+3-x+4x-3\sqrt{x}-3}{x+3\sqrt{x}}\)
\(=\dfrac{3x-2\sqrt{x}}{x+3\sqrt{x}}=\dfrac{3\sqrt{x}-2}{\sqrt{x}+3}\)
b: Khi \(x=20-6\sqrt{11}\) thì \(P=\dfrac{3\left(\sqrt{11}-3\right)-2}{\sqrt{11}-3+3}=\dfrac{3\sqrt{11}-9-2}{\sqrt{11}}=3-\sqrt{11}\)
