Question

Answer 1

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

Thay x = \(4-2\sqrt{3}\) vào P

\(\sqrt{4-2\sqrt{3}}+1=\sqrt{\left(\sqrt{3}-1\right)^2}+1=\left|\sqrt{3}-1\right|+1=\sqrt{3}-1+1=\sqrt{3}\)

Vậy với x = \(4-2\sqrt{3}\) thì P =\(\sqrt{3}\)