\(A=\dfrac{\left(\sqrt{x}+1\right)\left(\sqrt{x}-2\right)-\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}{\left(\sqrt{x}-2\right)^2\left(\sqrt{x}+2\right)}\cdot\left(\sqrt{x}-4+\dfrac{4}{\sqrt{x}}\right)\)
\(=\dfrac{\left(x-\sqrt{x}-2\right)-\left(x+\sqrt{x}-2\right)}{\left(\sqrt{x}-2\right)^2\left(\sqrt{x}+2\right)}\cdot\dfrac{x-4\sqrt{x}+4}{\sqrt{x}}\)
\(=\dfrac{x-\sqrt{x}-2-x-\sqrt{x}+2}{\left(\sqrt{x}-2\right)^2\left(\sqrt{x}+2\right)}\cdot\dfrac{x-4\sqrt{x}+4}{\sqrt{x}}\)
\(=\dfrac{-2\sqrt{x}}{\sqrt{x}\left(\sqrt{x}+2\right)}=-\dfrac{2}{\sqrt{x}+2}\)
\(A=\left(\dfrac{\sqrt{x}+1}{x-4}-\dfrac{\sqrt{x}-1}{\left(\sqrt{x}-2\right)^2}\right)\left(\dfrac{\left(\sqrt{x}-4\right)\left(\sqrt{x}+4\right)}{\sqrt{x}+4}+\dfrac{4}{\sqrt{x}}\right)\\ =\left(\dfrac{\left(\sqrt{x}+1\right)\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-2\right)^2\left(\sqrt{x}+2\right)}-\dfrac{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}{\left(\sqrt{x}-2\right)^2\left(\sqrt{x}+2\right)}\right)\left(\dfrac{\sqrt{x}\left(\sqrt{x}-4\right)}{\sqrt{x}}+\dfrac{4}{\sqrt{x}}\right)\\ =\left(\dfrac{x-2\sqrt{x}+\sqrt{x}-2}{\left(\sqrt{x}-2\right)^2\left(\sqrt{x}+2\right)}-\dfrac{x+2\sqrt{x}-\sqrt{x}-2}{\left(\sqrt{x}-2\right)^2\left(\sqrt{x}+2\right)}\right)\left(\dfrac{x-4\sqrt{x}+4}{\sqrt{x}}\right)\\ =-\dfrac{2\sqrt{x}}{\left(\sqrt{x}-2\right)^2\left(\sqrt{x}+2\right)}.\dfrac{\left(\sqrt{x}-2\right)^2}{\sqrt{x}}\\ =-\dfrac{2}{\sqrt{x}+2}\)
