A3. Let $x \in \mathbb{R}$ and $x>0, x \neq 4, x \neq 9$. Which expression is equivalent to $\left((2+\sqrt{x})^{-1}+1\right)^{-1}$?
(A) $\frac{x+\sqrt{x}-6}{x-9}$
(B) $\frac{x-\sqrt{x}-6}{x-9}$
(C) $\frac{x-\sqrt{x}+6}{x-9}$
(D) $\frac{x-\sqrt{x}-6}{x-4}$
(E) $\frac{x-\sqrt{x}+6}{x-4}$
A3. $\left.\operatorname{Expr}(2+\sqrt{x})^{-1}+1\right)^{-1}$ can be transformed into $\mathrm{v}\left(\frac{1}{2+\sqrt{x}}+1\right)^{-1}=\left(\frac{3+\sqrt{x}}{2+\sqrt{x}}\right)^{-1}=\frac{2+\sqrt{x}}{3+\sqrt{x}}, x \neq 9, x \neq 4$. We further rationalize the expression and get $\frac{x-\sqrt{x}-6}{x-9}$. The correct answer is B.