Question

Rút gọn:

P = \(\left(1+\dfrac{\sqrt{x1}}{x+\sqrt{x}+1}\right):\dfrac{\sqrt{x}+1}{x\sqrt{x}-1}\)

Answer 1

\(P=\left(1+\dfrac{\sqrt{x}}{x+\sqrt{x}+1}\right):\dfrac{\sqrt{x}+1}{x\sqrt{x}-1}\left(x\ge0,x\ne1\right)\)

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

\(=\dfrac{\left(\sqrt{x}+1\right)^2}{x+\sqrt{x}+1}.\dfrac{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}{\sqrt{x}+1}=\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)=x-1\)

Answer 2

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

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

\(=x-1\)