`a)` Khi `x=81`
`->``A=(\sqrt{81}-5)/\sqrt{81}=(9-5)/9=4/9`
`b)` `P=A.B`
`->``P=(\sqrt{x}-5)/\sqrt{x}.(\sqrt{x}/(\sqrt{x}-5)-(3\sqrt{x})/(x-25))` `=(\sqrt{x}-5)/\sqrt{x}.(\sqrt{x}/(\sqrt{x}-5)-(3\sqrt{x})/((\sqrt{x}-5)(\sqrt{x}+5)))`
`=(\sqrt{x}-5)/\sqrt{x}.(\sqrt{x}(\sqrt{x}+5)-3\sqrt{x})/((\sqrt{x}-5)(\sqrt{x}+5))`
`=(x+5\sqrt{x}-3\sqrt{x})/(\sqrt{x}(\sqrt{x}+5))`
`=(x+2\sqrt{x})/(\sqrt{x}(\sqrt{x}+5))`
`=(\sqrt{x}(\sqrt{x}+2))/(\sqrt{x}(\sqrt{x}+5))`
`=(\sqrt{x}+2)/(\sqrt{x}+5)`
`->P=(\sqrt{x}+2)/(\sqrt{x}+5)` `(đpcm)`
`c)P` và `P^{2}`
`->P^{2}``=((\sqrt{x}+2)/(\sqrt{x}+5))^{2}`
`=(\sqrt{x}+2)^{2}/(\sqrt{x}+5)^{2}`
`=(x+4\sqrt{x}+4)/(x+10\sqrt{x}+25)`
do `(\sqrt{x}+2)/(\sqrt{x}+5)>(x+4\sqrt{x}+4)/(x+10\sqrt{x}+25)`
Vậy `P>P^{2}`
