a)\(ĐKXĐ:\left\{{}\begin{matrix}x\ne0\\x\ne\sqrt{3}\end{matrix}\right.\)
\(A=\left(\frac{\sqrt{3}}{x^2+x\sqrt{3}+3}+\frac{3}{x^3-\sqrt{27}}\right)\left(\frac{x}{\sqrt{3}}+\frac{\sqrt{3}}{x}+1\right)\)
\(\Leftrightarrow A=\left(\frac{\sqrt{3}\left(x-\sqrt{3}\right)}{\left(x-\sqrt{3}\right)\left(x^2+x\sqrt{3}+3\right)}+\frac{3}{\left(x-\sqrt{3}\right)\left(x^2+x\sqrt{3}+3\right)}\right)\left(\frac{x^2}{x\sqrt{3}}+\frac{3}{x\sqrt{3}}+\frac{x\sqrt{3}}{x\sqrt{3}}\right)\)
\(\Leftrightarrow A=\frac{x\sqrt{3}}{\left(x-\sqrt{3}\right)\left(x^2+x\sqrt{3}+3\right)}.\frac{x^2+x\sqrt{3}+3}{x\sqrt{3}}\)
\(\Leftrightarrow A=\frac{1}{x-\sqrt{3}}\)
b) Tại \(x=\sqrt{3}+2\)
\(\Rightarrow A=\frac{1}{\sqrt{3}+2-\sqrt{3}}=\frac{1}{2}\)