$$\frac { 3 + \sqrt { 5 } } { \sqrt { 7 } - \sqrt { 3 } }$$
$\frac{\sqrt{15}+\sqrt{35}+3\sqrt{3}+3\sqrt{7}}{4}\approx 5.730617371$
$$\frac{\left(3+\sqrt{5}\right)\left(\sqrt{7}+\sqrt{3}\right)}{\left(\sqrt{7}-\sqrt{3}\right)\left(\sqrt{7}+\sqrt{3}\right)}$$
$$\frac{\left(3+\sqrt{5}\right)\left(\sqrt{7}+\sqrt{3}\right)}{\left(\sqrt{7}\right)^{2}-\left(\sqrt{3}\right)^{2}}$$
$$\frac{\left(3+\sqrt{5}\right)\left(\sqrt{7}+\sqrt{3}\right)}{7-3}$$
$$\frac{\left(3+\sqrt{5}\right)\left(\sqrt{7}+\sqrt{3}\right)}{4}$$
$$\frac{3\sqrt{7}+3\sqrt{3}+\sqrt{5}\sqrt{7}+\sqrt{5}\sqrt{3}}{4}$$
$$\frac{3\sqrt{7}+3\sqrt{3}+\sqrt{35}+\sqrt{5}\sqrt{3}}{4}$$
$$\frac{3\sqrt{7}+3\sqrt{3}+\sqrt{35}+\sqrt{15}}{4}$$
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