\(A=\left[\dfrac{\sqrt{x}-2}{x-1}-\dfrac{\sqrt{x}+2}{x+2\sqrt{x}+1}\right]\left[\dfrac{x^2-2x+1}{2}\right]\)
\(A=\left[\dfrac{\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)^2}{\left(x-1\right)\left(\sqrt{x}+1\right)^2}-\dfrac{\left(\sqrt{x}+2\right)\left(x-1\right)}{\left(x-1\right)\left(\sqrt{x}+1\right)^2}\right]\) \(\left[\dfrac{\left(x-1\right)^2}{2}\right]\)
\(A=\left[\dfrac{\left(\sqrt{x}-2\right)\left(x+2\sqrt{x}+1\right)-\left(x\sqrt{x}-\sqrt{x}+2x-2\right)}{\left(x-1\right)\left(\sqrt{x}+1\right)^2}\right]\) \(\dfrac{\left(x-1\right)^2}{2}\)
\(A=\left[\dfrac{x\sqrt{x}+2x+\sqrt{x}-2x-4\sqrt{x}-2-x\sqrt{x}+\sqrt{x}-2x+2}{\left(x-1\right)\left(\sqrt{x}+1\right)^2}\right]\)
\(A=\dfrac{\left(x-1\right)\left(x-1\right)}{2}\)
\(A=\dfrac{-2x-2\sqrt{x}}{\left(x-1\right)\left(\sqrt{x}+1\right)^2}.\dfrac{\left(x-1\right)\left(x-1\right)}{2}\)
\(A=\dfrac{-2\sqrt{x}\left(\sqrt{x}+1\right)}{\left(\sqrt{x}+1\right)^2}.\dfrac{x-1}{2}\)
\(A=-\sqrt{x}\left(\sqrt{x}-1\right)\)
\(A>0\Leftrightarrow-\sqrt{x}\left(\sqrt{x}-1\right)>0\)
\(\Leftrightarrow\sqrt{x}-1< 0\) vì \(-\sqrt{x}< 0\) \(\forall x>0\)
\(\Leftrightarrow\sqrt{x}< 1\Leftrightarrow x< 1\)
kết hợp với \(ĐKXĐ:x>0;x\ne1\) ta có \(0< x< 1\) ( luôn đúng )
