Thay `x = 4-2sqrt3` biểu thức `P` thì :
`P = (4-2sqrt3+1)/(sqrt{4-2sqrt3}+1)`
`= (5-2sqrt3)/(sqrt{(sqrt1)^2-2*1sqrt3+(sqrt3)^2}+1)`
`= (5-2sqrt3)/(sqrt{(1-sqrt3)^2}+1)`
`= (5-2sqrt3)/(|1-sqrt3|+1)`
`= (5-2sqrt3)/(sqrt3-1+1)`
`= ((5-2sqrt3)sqrt3)/(sqrt3sqrt3)`
`= (5sqrt3-6)/3`
Vậy `P = (5sqrt3-6)/3` khi `x = 4 - 2sqrt3` .