Question

Answer 1

1: \(P=\dfrac{2x+2}{\sqrt{x}}+\dfrac{x+\sqrt{x}+1}{\sqrt{x}}-\dfrac{\sqrt{x}\left(x\sqrt{x}+1\right)}{x\left(\sqrt{x}+1\right)}\)

\(=\dfrac{2x+2+x+\sqrt{x}+1}{\sqrt{x}}-\dfrac{x-\sqrt{x}+1}{\sqrt{x}}\)

\(=\dfrac{3x+\sqrt{x}+3-x+\sqrt{x}-1}{\sqrt{x}}=\dfrac{2x+2\sqrt{x}+2}{\sqrt{x}}\)

2: Khi x=3-2căn 2 thì \(P=\dfrac{2\left(3-2\sqrt{2}\right)+2\left(\sqrt{2}-1\right)+2}{\sqrt{2}-1}\)

\(=\dfrac{6-4\sqrt{2}+2\sqrt{2}}{\sqrt{2}-1}=\dfrac{6-2\sqrt{2}}{\sqrt{2}-1}=\left(6-2\sqrt{2}\right)\left(\sqrt{2}+1\right)\)

\(=6\sqrt{2}+6-4-2\sqrt{2}=4\sqrt{2}+2\)