Question

giải chi tiết 

Answer 1

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

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

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

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