`***`Lời giải`***`
a)
ĐKXĐ: `x≥0;xne9`
Ta có:` x=1/4`(N)
`=>A=\frac{\sqrt{1/4} +1}{\sqrt{1/4} -3}=\frac{1/2+1}{1/2 -3}=\frac{3/2}{-5/2}=-3/5`
b)
`B=\frac{x-3}{x-9}+\frac{1}{\sqrt{x}+3}-\frac{2}{3-\sqrt{x}}`
ĐKXĐ:`x≥0;xne9`
`=\frac{x-3}{x-9}+\frac{1}{\sqrt{x}+3}+\frac{2}{\sqrt{x}-3}`
`=\frac{x-3+\sqrt{x}-3+2(\sqrt{x}+3)}{x-9}`
`=\frac{x-3+\sqrt{x}-3+2\sqrt{x}+6}{x-9}`
`=\frac{x+3\sqrt{x}}{x-9}`
`=\frac{\sqrt{x}(\sqrt{x}+3)}{x-9}`
`=\frac{\sqrt{x}}{\sqrt{x}-3}`
Vậy `B=\frac{\sqrt{x}}{\sqrt{x}-3}` với `x≥0;xne9`
c)
`P=\frac{\sqrt{x}}{\sqrt{x}-3}:\frac{\sqrt{x} +1}{\sqrt{x} -3}`
`=\frac{\sqrt{x}}{\sqrt{x}-3}.\frac{\sqrt{x} -3}{ \sqrt{x} +1 }`
`=\frac{\sqrt{x}}{ \sqrt{x} +1 }`
Ta có: `\frac{\sqrt{x}}{ \sqrt{x} +1 }-1`
`=\frac{\sqrt{x}-(\sqrt{x} +1 )}{ \sqrt{x} +1 }`
`=\frac{\sqrt{x}-\sqrt{x} -1 }{ \sqrt{x} +1 }`
`=\frac{-1 }{ \sqrt{x} +1 }`
Ta có: `-1<0` và `\sqrt{x} +1>0`
`=>` `\frac{\sqrt{x}}{ \sqrt{x} +1 }-1<0`
`<=>\frac{\sqrt{x}}{ \sqrt{x} +1 }<1`
Vậy `P<1` với `x≥0;xne9`
