Question

Rút gọn biểu thức

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

Answer 1

\(x\ge0,x\ne4\)

\(=>A=\left[\dfrac{\left(x-\sqrt{x}+2\right)\sqrt{x}-x\left(\sqrt{x}+1\right)}{\sqrt{x}\left(\sqrt{x}+1\right)\left(\sqrt{x}-2\right)}\right].\dfrac{\sqrt{x}-2}{\sqrt{x}-1}\)

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

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