ĐK để A có nghĩa: x>1.
\(A=\dfrac{1}{x^2-\sqrt{x}}:\dfrac{\sqrt{x}+1}{x\sqrt{x}+x+\sqrt{x}}=\dfrac{1}{\sqrt{x}\left(x\sqrt{x}-1\right)}.\dfrac{\sqrt{x}\left(x+\sqrt{x}+1\right)}{\sqrt{x}+1}=\dfrac{1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}.\dfrac{x+\sqrt{x}+1}{\sqrt{x}+1}=\dfrac{1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}=\dfrac{1}{x-1}\)