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\(A=\left(\frac{\sqrt{x}}{\sqrt{x}+3}+\frac{x+9}{\left(3-\sqrt{x}\right)\left(3+\sqrt{x}\right)}\right).\frac{\sqrt{x}\left(\sqrt{x}-3\right)}{2\left(\sqrt{x}+2\right)}\)
\(=\frac{\sqrt{x}\left(3-\sqrt{x}\right)+x+9}{\left(3+\sqrt{x}\right)\left(3-\sqrt{x}\right)}.\frac{\sqrt{x}\left(\sqrt{x}-3\right)}{2\left(\sqrt{x}+2\right)}\)
\(=\frac{3\sqrt{x}-x+x+9}{\left(3+\sqrt{x}\right)\left(3-\sqrt{x}\right)}.\frac{\sqrt{x}\left(\sqrt{x}-3\right)}{2\left(\sqrt{x}+2\right)}\)
\(=\frac{3\left(\sqrt{x}+3\right)}{\left(3+\sqrt{x}\right)\left(3-\sqrt{x}\right)}.\frac{-\sqrt{x}\left(3-\sqrt{x}\right)}{2\left(\sqrt{x}+2\right)}\)
\(=\frac{-3\sqrt{x}}{2\left(\sqrt{x}+2\right)}\)
\(A^3=x^3-3x+3A\sqrt[3]{\frac{\left(x^3-3x\right)^2-\left(x^2-1\right)^2\left(x^2-4\right)}{4}}\)
\(A^3=x^3-3x+3A\sqrt[3]{\frac{x^6-6x^4+9x^2-\left(x^6-6x^4+9x^2-4\right)}{4}}\)
\(A^3=x^3-3x+3A\)
\(A^3-x^3-3\left(A-x\right)=0\)
\(\left(A-x\right)\left(A^2+x^2+Ax-3\right)=0\)
\(\Rightarrow A=x\) (do \(\left\{{}\begin{matrix}A>0\\x\ge2\end{matrix}\right.\) \(\Rightarrow x^2-3>0\Rightarrow A^2+x^2+Ax-3>0\))
2/ \(a+1=\sqrt{17}\Rightarrow a^2+2a+1=17\Rightarrow a^2+2a-17=-1\)
\(P=\left[a^3\left(a^2+2a-17\right)-a^2+18a-17\right]^{2018}\)
\(=\left(-a^3-a^2+18a-17\right)^{2018}\)
\(=\left(-a\left(a^2+2a-17\right)+a^2+a-17\right)^{2018}\)
\(=\left(a^2+2a-17\right)^{2018}\)
\(=\left(-1\right)^{2018}=1\)