a: Đặt \(A=\dfrac{\sqrt{x}+1}{\sqrt{2x}+1}+\dfrac{\sqrt{2x}+\sqrt{x}}{\sqrt{2x}-1}-1\)
\(=\dfrac{\left(\sqrt{x}+1\right)\left(\sqrt{2x}-1\right)+\left(\sqrt{2x}+\sqrt{x}\right)\left(\sqrt{2x}+1\right)-2x+1}{2x-1}\)
\(=\dfrac{x\sqrt{2}-\sqrt{x}+\sqrt{2x}-1+2x+\sqrt{2x}+x\sqrt{2}+\sqrt{x}-2x+1}{2x-1}\)
\(=\dfrac{2x\sqrt{2}+2\sqrt{2x}}{2x-1}\)
Đặt \(B=1+\dfrac{\sqrt{x}+1}{\sqrt{2x}+1}-\dfrac{\sqrt{2x}+\sqrt{x}}{\sqrt{2x}-1}\)
\(=\dfrac{2x-1+\left(\sqrt{x}+1\right)\left(\sqrt{2x}-1\right)-\left(\sqrt{2x}+\sqrt{x}\right)\left(\sqrt{2x}+1\right)}{2x-1}\)
\(=\dfrac{2x-1+x\sqrt{2}-\sqrt{x}+\sqrt{2x}-1-2x-\sqrt{2x}-x\sqrt{2}-\sqrt{x}}{2x-1}\)
\(=\dfrac{-2-2\sqrt{x}}{2x-1}\)
\(P=\dfrac{2\sqrt{2x}\left(\sqrt{x}+1\right)}{2x-1}:\dfrac{-2\left(\sqrt{x}+1\right)}{2x-1}\)
\(=\dfrac{-2\sqrt{2x}\left(\sqrt{x}+1\right)}{2\left(\sqrt{x}+1\right)}=-\sqrt{2x}\)
b: Khi x=1/2(3+2căn 2) thì \(P=-\sqrt{2\cdot\dfrac{1}{2}\left(3+2\sqrt{2}\right)}=-\sqrt{3+2\sqrt{2}}=-\sqrt{2}-1\)
