$$\frac{3}{5\sqrt{3}}+\frac{2}{5+\sqrt{3}}$$
$\frac{6\sqrt{3}}{55}+\frac{5}{11}\approx 0.643496452$
$$\frac{3\sqrt{3}}{5\left(\sqrt{3}\right)^{2}}+\frac{2}{5+\sqrt{3}}$$
$$\frac{3\sqrt{3}}{5\times 3}+\frac{2}{5+\sqrt{3}}$$
$$\frac{\sqrt{3}}{5}+\frac{2}{5+\sqrt{3}}$$
$$\frac{\sqrt{3}}{5}+\frac{2\left(5-\sqrt{3}\right)}{\left(5+\sqrt{3}\right)\left(5-\sqrt{3}\right)}$$
$$\frac{\sqrt{3}}{5}+\frac{2\left(5-\sqrt{3}\right)}{5^{2}-\left(\sqrt{3}\right)^{2}}$$
$$\frac{\sqrt{3}}{5}+\frac{2\left(5-\sqrt{3}\right)}{25-3}$$
$$\frac{\sqrt{3}}{5}+\frac{2\left(5-\sqrt{3}\right)}{22}$$
$$\frac{\sqrt{3}}{5}+\frac{1}{11}\left(5-\sqrt{3}\right)$$
$$\frac{\sqrt{3}}{5}+\frac{1}{11}\times 5+\frac{1}{11}\left(-1\right)\sqrt{3}$$
$$\frac{\sqrt{3}}{5}+\frac{5}{11}+\frac{1}{11}\left(-1\right)\sqrt{3}$$
$$\frac{\sqrt{3}}{5}+\frac{5}{11}-\frac{1}{11}\sqrt{3}$$
$$\frac{6}{55}\sqrt{3}+\frac{5}{11}$$
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$\frac{6 \sqrt{3} + 25}{55} = 0.6434964517347866$
