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