`#tnvt`
`\frac{1}{x-\sqrt{x}+1}(x>=0)`
`=\frac{1}{x-2.\sqrt{x}. 1/2+1/4+3/4}`
`=\frac{1}{(\sqrt{x}-1/2)^2+3/4}`
`∀x>=0,` ta có: `(\sqrt{x}-1/2)^2>=0`
`=>(\sqrt{x}-1/2)^2+3/4>=3/4`
`->\frac{1]{(\sqrt{x}-1/2)^2+3/4}<=1:3/4=4/3`
Dấu `=` xảy ra khi `(\sqrt{x}-1/2)^2=0<=>x=1/4`
Vậy `GTLNN=4/3` khi `x=1/4`