\(ĐKXĐ:x\ge0;x\ne\pm1\)
\(\left(\dfrac{\sqrt{x}-1}{\sqrt{x}+1}-\dfrac{\sqrt{x}+1}{\sqrt{x}-1}\right).\left(\dfrac{1}{2\sqrt{x}}-\dfrac{\sqrt{x}}{2}\right)^2=\dfrac{1-x}{\sqrt{x}}\)
\(\Leftrightarrow\dfrac{\left(\sqrt{x}-1\right)^2-\left(\sqrt{x}+1\right)^2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}.\left(\dfrac{2x-2}{4\sqrt{x}}\right)^2=\dfrac{1-x}{\sqrt{x}}\)
\(\Leftrightarrow\dfrac{\left(x-2\sqrt{x}+1\right)-\left(x+2\sqrt{x}+1\right)}{x-1}.\left(\dfrac{x-1}{2\sqrt{x}}\right)^2=\dfrac{1-x}{\sqrt{x}}\)
\(\Leftrightarrow\dfrac{-4\sqrt{x}}{x-1}.\dfrac{\left(x-1\right)^2}{4x}=\dfrac{1-x}{\sqrt{x}}\)
\(\Leftrightarrow\dfrac{-\left(x-1\right)}{\sqrt{x}}=\dfrac{1-x}{\sqrt{x}}\left(đúng\right)\)
Vậy ta có đpcm.