Bài 1: \(P=\dfrac{\sqrt{x}+1}{x-1}-\dfrac{x+2}{x\sqrt{x}-1}-\dfrac{\sqrt{x}+1}{x+\sqrt{x}+1}\)
a.Rút gọn P
b, Tìm MaxQ = \(\dfrac{2}{P}+\sqrt{x}\)
Bài 2:
\(P=\left(1-\dfrac{1-3\sqrt{x}}{x-9}\right):\left(\dfrac{9-x}{x+\sqrt{x}+6}-\dfrac{\sqrt{x}-3}{2-\sqrt{x}}-\dfrac{\sqrt{x}-3}{\sqrt{x}+3}\right)\)
a, Rút gọn P
b, Tìm x để P > 0
c, Max Q = P(x+1)
Bài 3:\(P=\dfrac{x-\sqrt{x}}{x+\sqrt{x}+1}-\dfrac{2x+\sqrt{x}}{\sqrt{x}}+\dfrac{2\left(x-1\right)}{\sqrt{x}-1}\)
a, Rút gọn P
b, Tìm x để \(Q=\dfrac{2\sqrt{x}}{P}\) nhận giá trị nguyên
Bài 4: Rút gọn: \(P=\left(2-\dfrac{\sqrt{x}-1}{2\sqrt{x}-3}\right):\left(\dfrac{6\sqrt{x}+1}{2x-\sqrt{x}-3}+\dfrac{\sqrt{x}}{\sqrt{x+1}}\right)\)