`a)`Thay `x=16` vào `B` ta được :
`(\sqrt{16}+3)/(16+\sqrt{16}+1)`
`=(4+3)/(16+4+1)`
`=7/21`
`=1/3`
Vậy `x=16` thì `B=1/3`
`b) P=A:B` `(ĐK:xge0;xne1)`
`->((2x+1)/(x\sqrt{x}-1)-1/(\sqrt{x}-1)):(\sqrt{x}+3)/(x+\sqrt{x}+1)`
`->((2x+1)/((\sqrt{x}-1)(x+\sqrt{x}+1))-1/(\sqrt{x}-1)).(x+\sqrt{x}+1)/(\sqrt{x}+3)`
`->(2x+1-(x+\sqrt{x}+1))/((\sqrt{x}-1)(x+\sqrt{x}+1)).(x+\sqrt{x}+1)/(\sqrt{x}+3)`
`->(2x+1-x-\sqrt{x}-1)/((\sqrt{x}-1)(\sqrt{x}+3))`
`->(x-\sqrt{x})/((\sqrt{x}-1)(\sqrt{x}+3))`
`->(\sqrt{x}(\sqrt{x}-1))/((\sqrt{x}-1)(\sqrt{x}+3))`
`->\sqrt{x}/(\sqrt{x}+3)`
`c)P<1/2`
`->\sqrt{x}/(\sqrt{x}+3)<1/2`
`->\sqrt{x}/(\sqrt{x}+3)-1/2<0`
`->(2\sqrt{x}-\sqrt{x}-3)/(2(\sqrt{x}+3))<0`
`->(\sqrt{x}-3)/(2(\sqrt{x}+3))<0`
Vì `2(\sqrt{x}+3)>0`
`->\sqrt{x}-3<0`
`->\sqrt{x}<3`
`->x<9`
Vậy `0lex<9` thì `P<1/2`
