$$\frac{\sqrt{3}}{3+9\sqrt{3}}$$
$-\frac{\sqrt{3}}{78}+\frac{3}{26}\approx 0.093178836$
$$\frac{\sqrt{3}\left(3-9\sqrt{3}\right)}{\left(3+9\sqrt{3}\right)\left(3-9\sqrt{3}\right)}$$
$$\frac{\sqrt{3}\left(3-9\sqrt{3}\right)}{3^{2}-\left(9\sqrt{3}\right)^{2}}$$
$$\frac{\sqrt{3}\left(3-9\sqrt{3}\right)}{9-\left(9\sqrt{3}\right)^{2}}$$
$$\frac{\sqrt{3}\left(3-9\sqrt{3}\right)}{9-9^{2}\left(\sqrt{3}\right)^{2}}$$
$$\frac{\sqrt{3}\left(3-9\sqrt{3}\right)}{9-81\left(\sqrt{3}\right)^{2}}$$
$$\frac{\sqrt{3}\left(3-9\sqrt{3}\right)}{9-81\times 3}$$
$$\frac{\sqrt{3}\left(3-9\sqrt{3}\right)}{9-243}$$
$$\frac{\sqrt{3}\left(3-9\sqrt{3}\right)}{-234}$$
$$\frac{3\sqrt{3}-9\left(\sqrt{3}\right)^{2}}{-234}$$
$$\frac{3\sqrt{3}-9\times 3}{-234}$$
$$\frac{3\sqrt{3}-27}{-234}$$
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