Question

Answer 1

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

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

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

b: Thay \(x=7-4\sqrt{3}\) vào P, ta được:

\(P=-\left(2-\sqrt{3}\right)\left(1-\sqrt{3}\right)\)

\(=\left(\sqrt{3}-2\right)\left(1-\sqrt{3}\right)\)

\(=\sqrt{3}-3-2+2\sqrt{3}=3\sqrt{3}-5\)