Question

đề là rút gọn nhé. mn giup em với

Answer 1

Giải:

Ta có:

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

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

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

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

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