Bài `6`

`A=(x+\sqrt{x}-6)/(x-9)+(x-7\sqrt{x}+19)/(x+\sqrt{x}-12)-(x-5\sqrt{x})/(x+4\sqrt{x})`

`A=(x+3\sqrt{x}-2\sqrt{x}-6)/((\sqrt{x}-3)(\sqrt{x}+3))+(x-7\sqrt{x}+19)/(x+4\sqrt{x}-3\sqrt{x}-12)-(x-5\sqrt{x})/(\sqrt{x}(\sqrt{x}+4))`

`A=((\sqrt{x}-2)(\sqrt{x}+3))/((\sqrt{x}-3)(\sqrt{x}+3))+(x-7\sqrt{x}+19)/((\sqrt{x}-3)(\sqrt{x}+4))-(\sqrt{x}(\sqrt{x}-5))/(\sqrt{x}(\sqrt{x}+4))`

`A=(\sqrt{x}-2)/(\sqrt{x}-3)+(x-7\sqrt{x}+19)/((\sqrt{x}-3)(\sqrt{x}+4))-(\sqrt{x}-5)/(\sqrt{x}+4)`

`A=((\sqrt{x}-2)(\sqrt{x}+4)+x-7\sqrt{x}+19-(\sqrt{x}-5)(\sqrt{x}-3))/((\sqrt{x}-3)(\sqrt{x}+4))`

`A=(x+3\sqrt{x}-4)/((\sqrt{x}-3)(\sqrt{x}+4))`

`A=(x-\sqrt{x}+4\sqrt{x}-4)/((\sqrt{x}-3)(\sqrt{x}+4))`

`A=(\sqrt{x}(\sqrt{x}-1)+4(\sqrt{x}-1))/((\sqrt{x}-3)(\sqrt{x}+4))`

`A=((\sqrt{x}+4)(\sqrt{x}-1))/((\sqrt{x}-3)(\sqrt{x}+4))`

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

Câu `7`

`a)`

`P=(3x+5\sqrt{x}-4)/((\sqrt{x}+3)(\sqrt{x}-1))-(\sqrt{x}+1)/(\sqrt{x}+3)-(\sqrt{x}+3)/(\sqrt{x}-1)`

`P=(3x+5\sqrt{x}-4-(\sqrt{x}+1)(\sqrt{x}-1)-(\sqrt{x}+3)^2)/((\sqrt{x}+3)(\sqrt{x}-1))`

`P=(3x+5\sqrt{x}-4-x+1-x-6\sqrt{x}-9)/((\sqrt{x}+3)(\sqrt{x}-1))`

`P=(x-\sqrt{x}-12)/((\sqrt{x}+3)(\sqrt{x}-1))`

`P=(x-4\sqrt{x}+3\sqrt{x}-12)/((\sqrt{x}+3)(\sqrt{x}-1))`

`P=((\sqrt{x}+3)(\sqrt{x}-4))/((\sqrt{x}+3)(\sqrt{x}-1))`

`P=(\sqrt{x}-4)/(\sqrt{x}-1)`

`b)`

Thay `P=1/2`, ta có:

`(\sqrt{x}-4)/(\sqrt{x}-1)=1/2`

`\sqrt{x}-1=2(\sqrt{x}-4)`

`\sqrt{x}-1=2\sqrt{x}-8`

`\sqrt{x}-2\sqrt{x}=-8+1`

`-\sqrt{x}=-7`

`\sqrt{x}=7`

`x=49 (TM)`

Vậy `x=49`