$$\frac{\sqrt{3}}{3+2\sqrt{3}}$$
$2-\sqrt{3}\approx 0.267949192$
$$\frac{\sqrt{3}\left(3-2\sqrt{3}\right)}{\left(3+2\sqrt{3}\right)\left(3-2\sqrt{3}\right)}$$
$$\frac{\sqrt{3}\left(3-2\sqrt{3}\right)}{3^{2}-\left(2\sqrt{3}\right)^{2}}$$
$$\frac{\sqrt{3}\left(3-2\sqrt{3}\right)}{9-\left(2\sqrt{3}\right)^{2}}$$
$$\frac{\sqrt{3}\left(3-2\sqrt{3}\right)}{9-2^{2}\left(\sqrt{3}\right)^{2}}$$
$$\frac{\sqrt{3}\left(3-2\sqrt{3}\right)}{9-4\left(\sqrt{3}\right)^{2}}$$
$$\frac{\sqrt{3}\left(3-2\sqrt{3}\right)}{9-4\times 3}$$
$$\frac{\sqrt{3}\left(3-2\sqrt{3}\right)}{9-12}$$
$$\frac{\sqrt{3}\left(3-2\sqrt{3}\right)}{-3}$$
$$\frac{3\sqrt{3}-2\left(\sqrt{3}\right)^{2}}{-3}$$
$$\frac{3\sqrt{3}-2\times 3}{-3}$$
$$\frac{3\sqrt{3}-6}{-3}$$
$$-\sqrt{3}+2$$
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