\(a,B=\dfrac{2\sqrt{x}+x-x-\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\cdot\dfrac{x+\sqrt{x}+1}{\sqrt{x}+2}\\ B=\dfrac{\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}=\dfrac{1}{\sqrt{x}+2}\\ b,x=4+2\sqrt{3}\Leftrightarrow\sqrt{x}=\sqrt{\left(\sqrt{3}+1\right)^2}=\sqrt{3}+1\\ \Leftrightarrow B=\dfrac{1}{\sqrt{3}+1+2}=\dfrac{1}{\sqrt{3}+3}=\dfrac{3-\sqrt{3}}{6}\\ c,B=\dfrac{1}{\sqrt{x}+2}\le\dfrac{1}{0+2}=\dfrac{1}{2}\\ B_{max}=\dfrac{1}{2}\Leftrightarrow x=0\)
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