\(A=\left[\dfrac{2x-4\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}-\dfrac{\left(\sqrt{x}-2\right)\left(2\sqrt{x}-1\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\right]:\dfrac{\sqrt{x}}{\sqrt{x}-2}+1\)
\(=\left[\dfrac{2x-4\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}-\dfrac{2x-5\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\right].\left(\dfrac{\sqrt{x}-2}{\sqrt{x}}\right)+1\)
\(=\left(\dfrac{\sqrt{x}}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\right).\dfrac{\sqrt{x}-2}{\sqrt{x}}+1\)
\(=\dfrac{1}{\sqrt{x}+2}+1=\dfrac{\sqrt{x}+3}{\sqrt{x}+2}\)
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