đk x >= 0 ; x khác 1
a, \(\left(\dfrac{\sqrt{x}-2}{x-1}-\dfrac{\sqrt{x}+2}{\left(\sqrt{x}+1\right)^2}\right)\left(\dfrac{\left(1-x\right)^2}{2}\right)\)
\(=\left(\dfrac{\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)-\left(\sqrt{x}+2\right)\left(\sqrt{x}-1\right)}{\left(x-1\right)\left(\sqrt{x}+1\right)}\right).\left(\dfrac{\left(1-x\right)^2}{2}\right)\)
\(=\dfrac{x-\sqrt{x}-2-\left(x+\sqrt{x}-2\right)}{\left(x-1\right)\left(\sqrt{x}+1\right)}\left(\dfrac{\left(1-x\right)^2}{2}\right)\)
\(=\dfrac{-2\sqrt{x}}{\left(\sqrt{x}+1\right)}.\dfrac{x-1}{2}=-\sqrt{x}\left(\sqrt{x}-1\right)=-x+\sqrt{x}\)
b, \(-x+\sqrt{x}=-\left(x-\sqrt{x}+\dfrac{1}{4}\right)+\dfrac{1}{4}=-\left(\sqrt{x}-\dfrac{1}{2}\right)^2+\dfrac{1}{4}\le\dfrac{1}{4}\)
Dấu ''='' xảy ra khi x = 1/4
