$$\frac { 3 + \sqrt { 5 } } { \sqrt { 13 } - \sqrt { 7 } }$$
$\frac{\sqrt{35}+\sqrt{65}+3\sqrt{7}+3\sqrt{13}}{6}\approx 5.455374215$
$$\frac{\left(3+\sqrt{5}\right)\left(\sqrt{13}+\sqrt{7}\right)}{\left(\sqrt{13}-\sqrt{7}\right)\left(\sqrt{13}+\sqrt{7}\right)}$$
$$\frac{\left(3+\sqrt{5}\right)\left(\sqrt{13}+\sqrt{7}\right)}{\left(\sqrt{13}\right)^{2}-\left(\sqrt{7}\right)^{2}}$$
$$\frac{\left(3+\sqrt{5}\right)\left(\sqrt{13}+\sqrt{7}\right)}{13-7}$$
$$\frac{\left(3+\sqrt{5}\right)\left(\sqrt{13}+\sqrt{7}\right)}{6}$$
$$\frac{3\sqrt{13}+3\sqrt{7}+\sqrt{5}\sqrt{13}+\sqrt{5}\sqrt{7}}{6}$$
$$\frac{3\sqrt{13}+3\sqrt{7}+\sqrt{65}+\sqrt{5}\sqrt{7}}{6}$$
$$\frac{3\sqrt{13}+3\sqrt{7}+\sqrt{65}+\sqrt{35}}{6}$$
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