Answer 1

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

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

`=(x-3\sqrt{x}+2+5\sqrt{x}-2)/((\sqrt{x}-2)(\sqrt{x}+2))`

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

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

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

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`ĐK:x>0;x\ne 4`

`P/Q=(x+3)/(\sqrt{x}-2):(\sqrt{x})/(\sqrt{x}-2)`

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

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

`=\sqrt{x}+(3)/(\sqrt{x})\ge 2\sqrt{\sqrt{x}.(3)/(\sqrt{x}}=2\sqrt{3}` (BĐT Cô Si)

Dấu ''='' xảy ra `<=>\sqrt{x}=3/\sqrt{x}<=>x=3` (TMDK)

Vậy GTNN `P/Q` là : `2\sqrt{3}` tại `x=3`