a) D (ĐKXĐ: x\(\ge0,x\ne1\))
=\(\left(\dfrac{2x-\sqrt{x}\left(x+\sqrt{x}+1\right)}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\right)\left(1-\sqrt{x}+x-\sqrt{x}\right)\)
=\(\dfrac{2x-x\sqrt{x}-x-\sqrt{x}}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}.\left(\sqrt{x}-1\right)^2\)
\(=\dfrac{\left(x-x\sqrt{x}-\sqrt{x}\right)\left(\sqrt{x}-1\right)}{\left(x+\sqrt{x}+1\right)}\)
=\(\dfrac{\sqrt{x}\left(\sqrt{x}-x-1\right)\left(\sqrt{x}-1\right)}{\left(x+\sqrt{x}+1\right)}\)
=\(-\sqrt{x}\left(\sqrt{x}-1\right)=\sqrt{x}-x\)
b) \(\sqrt{x}-x=3\Leftrightarrow\sqrt{x}\left(1-\sqrt{x}\right)=3\)
=\(\sqrt{x}-x-3=0\Leftrightarrow\left(x-2.\dfrac{1}{2}x+\dfrac{1}{4}\right)-\dfrac{13}{4}=0\)
\(\left(\sqrt{x}-\dfrac{1}{2}\right)^2-\dfrac{13}{4}=0\)
\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x}-\dfrac{1}{2}=\dfrac{13}{4}\\\sqrt{x}-\dfrac{1}{2}=-\dfrac{13}{4}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{225}{16}\\x=\dfrac{121}{16}\end{matrix}\right.\)
