`21.`

`a)P=((2\sqrtx+x)/(x\sqrtx-1)-1/(\sqrtx-1)):(1-(\sqrtx+2)/(x+\sqrtx+1))` với `x>=0,x\ne1`

`= [ (2\sqrt{x} + x - (x + \sqrt{x} + 1)) / ((\sqrt{x} - 1)(x + \sqrt{x} + 1)) ] : [ (x + \sqrt{x} + 1 - (\sqrt{x} + 2)) / (x + \sqrt{x} + 1) ]`

`= [ (\sqrt{x} - 1) / ((\sqrt{x} - 1)(x + \sqrt{x} + 1)) ] : [ (x - 1) / (x + \sqrt{x} + 1) ]`

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

`= 1 / (x - 1)`

`b)` Thay `x = 5 + 2\sqrt{3}` vào `P` có : `P = 1 / (5 + 2\sqrt{3} - 1)`

`= 1 / (4 + 2\sqrt{3})`

`= 1 / ((\sqrt{3} + 1)^2)`

`-> \sqrt{P} = \sqrt{1 / ((\sqrt{3} + 1)^2)}= 1 / (\sqrt{3} + 1)= (\sqrt{3} - 1) / 2`