Đáp án+Giải thích các bước giải:

 `a)A=((\sqrt{x}-1)/(3\sqrt{x}-1)-(1)/(3\sqrt{x}+1)+(8\sqrt{x})/(9\sqrt{x}-1)):((1-3\sqrt{x}-2)/(3\sqrt[x}+1))`

`( đ k : x\ge0;x\ne 1/9)`

`=[((\sqrt{x}-1).(3\sqrt{x}+1))/((3\sqrt{x}-1).(3\sqrt{x}+1))-(3\sqrt{x}-1)/((3\sqrt{x}-1).(3\sqrt{x}+1))+(8\sqrt{x})/((3\sqrt{x}-1).(3\sqrt{x}+1))].(3\sqrt{x}+1)/(-3\sqrt{x}-1)`

`=[(3x+\sqrt{x}-3\sqrt{x}-1-3\sqrt{x}+1+8\sqrt{x})/((3\sqrt{x}-1).(3\sqrt{x}+1))].(3\sqrt{x}+1)/(-(3\sqrt{x}+1))`

`=(3x+3\sqrt{x})/((3\sqrt{x}-1).(3\sqrt{x}+1)). (-1)`

`=(3x+3\sqrt{x})/((3\sqrt{x})^{2}-1^{2}).(-1)`

`=(3x+3\sqrt{x})/(9x-1).(-1)`

`=(3x+3\sqrt{x})/(1-9x)`

Vậy `A=(3x+3\sqrt{x})/(1-9x)` với `x\ge0;x\ne 1/9`

`b)A=6/5`

`(3x+3\sqrt{x})/(1-9x)=6/5` `( đ k : x\ge0;x\ne1/9)`

`6.(1-9x)=5.(3x+3\sqrt{x})`

`6-54x=15x+15\sqrt{x}`

`15x+15\sqrt{x}+54x-6=0`

`69x+15\sqrt{x}-6=0`

`69.(x+(5)/(23).\sqrt{x}-2/23)=0`

`(\sqrt{x})^{2}+2.\sqrt{x}. (5)/(46)+((5)/(46))^{2}-2/23-((5)/(46))^{2}=0`

`(\sqrt{x}+(5)/(46))^{2}-(209)/(2116)=0`

`(\sqrt[x}+(5)/(46))^{2}=(\pm (\sqrt{209})/(46))^{2}`

`\sqrt{x}+(5)/(46)=-(\sqrt{209})/(46)` hoặc `\sqrt{x}+(5)/(46)=(\sqrt{209})/(46)`

`\sqrt{x}=(-5-\sqrt{209})/(46)` (Vô lí) hoặc `\sqrt{x}=(\sqrt{209}-5)/(46)`

`->x=((\sqrt[209}-5)/(46))^{2}`

`->x=(117-5\sqrt{209})/(1058)(tmđk)`

Vậy `x=(117-5\sqrt{209})/(1058)` để `A=6/5`