$$\frac{\sqrt{7}+2}{\sqrt{5}-\sqrt{3}}$$
$\frac{\sqrt{21}}{2}+\frac{\sqrt{35}}{2}+\sqrt{3}+\sqrt{5}\approx 9.217446524$
$$\frac{\left(\sqrt{7}+2\right)\left(\sqrt{5}+\sqrt{3}\right)}{\left(\sqrt{5}-\sqrt{3}\right)\left(\sqrt{5}+\sqrt{3}\right)}$$
$$\frac{\left(\sqrt{7}+2\right)\left(\sqrt{5}+\sqrt{3}\right)}{\left(\sqrt{5}\right)^{2}-\left(\sqrt{3}\right)^{2}}$$
$$\frac{\left(\sqrt{7}+2\right)\left(\sqrt{5}+\sqrt{3}\right)}{5-3}$$
$$\frac{\left(\sqrt{7}+2\right)\left(\sqrt{5}+\sqrt{3}\right)}{2}$$
$$\frac{\sqrt{7}\sqrt{5}+\sqrt{7}\sqrt{3}+2\sqrt{5}+2\sqrt{3}}{2}$$
$$\frac{\sqrt{35}+\sqrt{7}\sqrt{3}+2\sqrt{5}+2\sqrt{3}}{2}$$
$$\frac{\sqrt{35}+\sqrt{21}+2\sqrt{5}+2\sqrt{3}}{2}$$
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