`\qquad A=(1/(1-\sqrt{x})+(x+2)/(x\sqrt{x}-1)+\sqrt{x}/(x+\sqrt{x}+1)):(\sqrt{x}-1)/3`
Với `x>=0; x \ne 1`
`A=(-x-\sqrt{x}-1+x+2+\sqrt{x}(\sqrt{x}-1))/((\sqrt{x}-1)(x+\sqrt{x}+1)). 3/(\sqrt{x}-1)`
`A=(-\sqrt{x}+1+x-\sqrt{x})/((\sqrt{x}-1)(x+\sqrt{x}+1)). 3/(\sqrt{x}-1)`
`A=(3(x-2\sqrt{x}+1))/((\sqrt{x}-1)^2 (x+\sqrt{x}+1))`
`A=(3(\sqrt{x}-1)^2)/((\sqrt{x}-1)^2(x+\sqrt{x}+1))`
`A=3/(x+\sqrt{x}+1)`
Do `x>=0 => x+\sqrt{x}+1>=1`
`=> 3/(x+\sqrt{x}+1)<=3`
Dấu = xảy ra khi `x=0`
Vậy `A_(max)=3<=>x=0`
