Bài `8`

`1)`

`B=(2\sqrt{x}-3)/(\sqrt{x}-1)+(3-\sqrt{x})/(x-1) (x>0;x\ne1)`

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

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

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

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

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

`B=(2\sqrt{x})/(\sqrt{x}+1) (đpcm)`

`3)`

Để `A.B=4` thì

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

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

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

`x+2=2(\sqrt{x}+1)`

`x+2=2\sqrt{x}+2`

`x-2\sqrt{x}=0`

`\sqrt{x}(\sqrt{x}-2)=0`

`\sqrt{x}=0` hoặc `\sqrt{x}-2=0`

`x=0` hoặc `\sqrt{x}=2`

`x=0 (ktm)` hoặc `x=4 (tm)`

Vậy `x=4`

Bài `9`

`1)`

`B=(x+8\sqrt{x})/(x-4)+(\sqrt{x}-1)/(\sqrt{x}+2)+(\sqrt{x}+1)/(2-\sqrt{x}) (x>0;x\ne4)`

`B=(x+8\sqrt{x})/((\sqrt{x}-2)(\sqrt{x}+2))+(\sqrt{x}-1)/(\sqrt{x}+2)-(\sqrt{x}+1)/(\sqrt{x}-2)`

`B=(x+8\sqrt{x}+(\sqrt{x}-1)(\sqrt{x}-2)-(\sqrt{x}+1)(\sqrt{x}+2))/((\sqrt{x}-2)(\sqrt{x}+2))`

`B=(x+8\sqrt{x}+x-3\sqrt{x}+2-x-3\sqrt{x}-2)/((\sqrt{x}-2)(\sqrt{x}+2))`

`B=(x+2\sqrt{x})/((\sqrt{x}-2)(\sqrt{x}+2))`

`B=(\sqrt{x}(\sqrt{x}+2))/((\sqrt{x}-2)(\sqrt{x}+2))`

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

`2)`

`P=A:B`

`P=(2+\sqrt{x})/(\sqrt{x}) : (\sqrt{x})/(\sqrt{x}-2)`

`P=(2+\sqrt{x})/(\sqrt{x}) . (\sqrt{x}-2)/(\sqrt{x})`

`P=(x-4)/x`

Để `Px=3/2(\sqrt{x}-1)` thì

`(x-4)/x . x=3/2(\sqrt{x}-1)`

`x-4=3/2(\sqrt{x}-1)`

`2x-8=3(\sqrt{x}-1)`

`2x-8=3\sqrt{x}-3`

`2x-8-3\sqrt{x}+3=0`

`2x-3\sqrt{x}-5=0`

`2x-5\sqrt{x}+2\sqrt{x}-5=0`

`\sqrt{x}(2\sqrt{x}-5)+(2\sqrt{x}-5)=0`

`(\sqrt{x}+1)(2\sqrt{x}-5)=0`

`\sqrt{x}+1=0` hoặc `2\sqrt{x}-5=0`

`\sqrt{x}=-1` (vô lí) hoặc `\sqrt{x}=5/2`

`x=25/4 (tm)`

Vậy `x=25/4`