ĐKXĐ:
\(\left\{{}\begin{matrix}x\ge0\\1-x\ne0\\1+x\sqrt{x}\ne0\\2\sqrt{x}-1\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ge0\\x\ne1\\x\ne\dfrac{1}{4}\end{matrix}\right.\)
\(A=1-\left(\dfrac{2x-1+\sqrt{x}}{1-x}+\dfrac{2x\sqrt{x}+x-\sqrt{x}}{1+x\sqrt{x}}\right)\dfrac{\left(x-\sqrt{x}\right)\left(1-\sqrt{x}\right)}{2\sqrt{x}-1}\)
\(A=1-\left(\dfrac{\left(\sqrt{x}+1\right)\left(2\sqrt{x}-1\right)}{\left(1-\sqrt{x}\right)\left(1+\sqrt{x}\right)}+\dfrac{\sqrt{x}\left(\sqrt{x}+1\right)\left(2\sqrt{x}-1\right)}{\left(1+\sqrt{x}\right)\left(x-\sqrt{x}+1\right)}\right)\dfrac{\left(x-\sqrt{x}\right)\left(1-\sqrt{x}\right)}{2\sqrt{x}-1}\)
\(A=1-\left(\dfrac{1}{1-\sqrt{x}}+\dfrac{\sqrt{x}}{1-\sqrt{x}+x}\right)\left(x-\sqrt{x}\right)\left(1-\sqrt{x}\right)\)
\(A=1-\dfrac{1-\sqrt{x}+x+\sqrt{x}-x}{\left(1-\sqrt{x}\right)\left(1-\sqrt{x}+x\right)}\left(x-\sqrt{x}\right)\left(1-\sqrt{x}\right)\)
\(A=1-\dfrac{x-\sqrt{x}}{1-\sqrt{x}+x}=\dfrac{1-\sqrt{x}+x-x+\sqrt{x}}{1-\sqrt{x}+x}=\dfrac{1}{1-\sqrt{x}+x}\)
