__________Rút gọn
P = (x^2 - √x)/(x + √x + 1) - (2x + √x)/√x + 2(x - 1)/(√x - 1)
= (√x^4 - √x) / (x + √x + 1) - √x.(2√x + 1)/√x + 2(x - 1)/(√x - 1)
= √x(√x^3 - 1)/(x + √x + 1) - (2√x + 1) + 2(x - 1)/(√x - 1)
= √x(√x - 1)(x + √x + 1)/(x + √x + 1) - 2√x - 1 + [2(√x - 1)(√x + 1)]/(√x - 1)
= √x.(√x - 1) - 2√x - 1 + 2(√x + 1)
= x - √x - 2√x - 1 + 2√x + 2
= x - √x + 1
_______Để P = 3 ta có
x - √x + 1 = 3
<=> x - √x - 2 = 0
<=> x + √x - 2√x - 2 = 0
<=> √x(√x + 1) -2(√x + 1) = 0
<=> (√x - 2)(√x + 1) = 0
Mà √x + 1 > 0
<=> √x - 2 = 0
<=> √x = 2
<=> x = 4 (nhận)
​Vậy . . .
_________Tính P tại x = 7 + 2√3 
x + √x + 1 = 7 + 2√3 + √(7 + 2√3) + 1 = 7 + 2√3 + √(4 + 2√3 + 3)^2 + 1 = 8 + 2√3 + 2 + 2√3 = 10 + 4√3
_________Để P > 3 ta có
<=> x + √x + 1 > 3
<=> x + √x - 2 > 0
<=> x + √x - 2√x - 2 > 0
<=> √x(√x + 1) -2(√x + 1) > 0
<=> (√x - 2)(√x + 1) > 0
<=> √x > 2