\(a,A=\dfrac{\sqrt{x}\left(x\sqrt{x}+1\right)}{x-\sqrt{x}+1}-\dfrac{\sqrt{x}\left(2\sqrt{x}+1\right)}{\sqrt{x}}+3\\ A=\dfrac{\sqrt{x}\left(\sqrt{x}+1\right)\left(x-\sqrt{x}+1\right)}{x-\sqrt{x}+1}-2\sqrt{x}-1+3\\ A=x+\sqrt{x}-2\sqrt{x}+2=x-\sqrt{x}+2\\ b,A=\left(x-\sqrt{x}+\dfrac{1}{4}\right)+\dfrac{7}{4}=\left(\sqrt{x}-\dfrac{1}{2}\right)^2+\dfrac{7}{4}\ge\dfrac{7}{4}\\ A_{min}=\dfrac{7}{4}\Leftrightarrow\sqrt{x}=\dfrac{1}{2}\Leftrightarrow x=\dfrac{1}{4}\left(tm\right)\)
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