Bài `6`

`a)`

`A=(2\sqrt{x})/(x-9)-2/(\sqrt{x}+3) (x>=0;x\ne9)`

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

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

`A=(2\sqrt{x}-2\sqrt{x}+6)/((\sqrt{x}-3)(\sqrt{x}+3))`

`A=6/(x-9)`

`b)`

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

`6/(x-3\sqrt{x}):6/(x-9)=(2\sqrt{x}+1)/2`

`6/(\sqrt{x}(\sqrt{x}-3)) . ((\sqrt{x}-3)(\sqrt{x}+3))/6=(2\sqrt{x}+1)/2`

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

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

`2\sqrt{x}+6=2x+\sqrt{x}`

`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` hoặc `\sqrt{x}-2=0`

`\sqrt{x}=-3/2` (vô lí) hoặc `\sqrt{x}=2`

`x=4 (tm)`

Vậy `x=4`

Bài `7`

`a)`

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

`P=[(x-2)/(\sqrt{x}(\sqrt{x}+2))+1/(\sqrt{x}+2)] . (\sqrt{x}+1)/(\sqrt{x}-1)`

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

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

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

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

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

`b)`

Để `2P=2\sqrt{x}+5` thì

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

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

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

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

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

`2x+4\sqrt{x}-\sqrt{x}-2=0`

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

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

`2\sqrt{x}-1=0` hoặc `\sqrt{x}+2=0`

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

`x=1/4 (tm)`

Vậy `x=1/4`