`P=\frac{2\sqrt{x}}{x-9}-\frac{2}{\sqrt{x}+3}`
`=> P=\frac{2\sqrt{x}}{(\sqrt{x}+3)(\sqrt{x}-3)}-\frac{2}{\sqrt{x}+3}`
`=> P=\frac{2\sqrt{x}-2(\sqrt{x}-3)}{x-9}`
`=> P=\frac{2\sqrt{x}-2\sqrt{x}+6}{x-9}`
`=> P=\frac{6}{x-9}`
`Q=\frac{6}{x-3\sqrt{x}}`
`=> Q=\frac{6}{\sqrt{x}(\sqrt{x}-3)}`
Do `A=\frac{Q}{P}`
`=>` $A=\dfrac{\dfrac{6}{\sqrt{x}(\sqrt{x}-3)}}{\dfrac{6}{x-9}}$
`=> A\frac{6}{\sqrt{x}(\sqrt{x}-3)}.\frac{(\sqrt{x}-3)(\sqrt{x}+3)}{6}`
`=> A=\frac{\sqrt{x}+3}{\sqrt{x}}`
Để `A` `=\frac{2\sqrt{x}+1}{2}` :
ĐKXĐ: `x\ ge 0, x\ne 9`
`=> \frac{2\sqrt{x}+1}{2}=\frac{\sqrt{x}+3}{\sqrt{x}}`
`=> 2x+\sqrt{x}=2\sqrt{x}+6`
`<=> 2x-\sqrt{x}-6=0`
`<=> 2x-4\sqrt{x}+ 3\sqrt{x}-6=0`
`<=> 2\sqrt{x}(\sqrt{x}-2)+3(\sqrt{x}-2)=0`
`<=> (2\sqrt{x}+3)(\sqrt{x}-2)=0`
`(2\sqrt{x}+3)=0`
`=> ` Vô nghiệm
`=> \sqrt{x}-2=0`
`<=> x=4`
Vậy để `A=\frac{2\sqrt{x}+1}{2}` thì `x=4`.
