Ta có: \(\dfrac{2\sqrt{x}}{\sqrt{x^3}+\sqrt{x}-x-1}-\dfrac{1}{\sqrt{x}-1}\)
\(=\dfrac{2\sqrt{x}}{\left(x+1\right)\left(\sqrt{x}-1\right)}-\dfrac{x+1}{\left(\sqrt{x}-1\right)\left(x+1\right)}\)
\(=\dfrac{-x+2\sqrt{x}-1}{\left(x+1\right)\left(\sqrt{x}-1\right)}\)
\(=\dfrac{-\left(\sqrt{x}-1\right)^2}{\left(x+1\right)\left(\sqrt{x}-1\right)}\)
\(=\dfrac{1-\sqrt{x}}{x+1}\)
\(A=\dfrac{2\sqrt{x}}{x\sqrt{x}+\sqrt{x}-x-1}-\dfrac{1}{\sqrt{x}-1}\\ =\dfrac{2\sqrt{x}}{\left(\sqrt{x}-1\right)\left(x+1\right)}-\dfrac{1}{\sqrt{x}-1}\\ =\dfrac{2\sqrt{x}-x-1}{\left(\sqrt{x}-1\right)\left(x+1\right)}\\ =\dfrac{-\left(\sqrt{x}-1\right)^2}{\left(\sqrt{x}-1\right)\left(x+1\right)}=\dfrac{-\left(\sqrt{x}-1\right)}{\left(x+1\right)}\\ =\dfrac{1-\sqrt{x}}{x+1}\)
Ta có:\(\dfrac{2\sqrt{x}}{\sqrt{x^3}+\sqrt{x}-x-1}-\dfrac{1}{\sqrt{x}-1}\)
\(=\dfrac{2\sqrt{x}}{\sqrt{x}\left(x+1\right)-\left(x+1\right)}-\dfrac{1}{\sqrt{x}-1}\)
\(=\dfrac{2\sqrt{x}}{\left(x+1\right)\left(\sqrt{x}-1\right)}-\dfrac{x+1}{\left(x+1\right)\left(\sqrt{x}-1\right)}\)
\(\dfrac{-\left(x-2\sqrt{x}+1\right)}{\left(x+1\right)\left(\sqrt{x}-1\right)}=\dfrac{-\left(\sqrt{x}-1\right)^2}{\left(x+1\right)\left(\sqrt{x}-1\right)}=-\dfrac{\left(\sqrt{x}-1\right)}{x+1}\)
