$$\frac{ \sqrt{ 4 } + \sqrt{ 5 } }{ \sqrt{ 5 } - \sqrt{ 3 } }$$
$\frac{\sqrt{15}}{2}+\sqrt{3}+\sqrt{5}+\frac{5}{2}\approx 8.404610458$
$$\frac{2+\sqrt{5}}{\sqrt{5}-\sqrt{3}}$$
$$\frac{\left(2+\sqrt{5}\right)\left(\sqrt{5}+\sqrt{3}\right)}{\left(\sqrt{5}-\sqrt{3}\right)\left(\sqrt{5}+\sqrt{3}\right)}$$
$$\frac{\left(2+\sqrt{5}\right)\left(\sqrt{5}+\sqrt{3}\right)}{\left(\sqrt{5}\right)^{2}-\left(\sqrt{3}\right)^{2}}$$
$$\frac{\left(2+\sqrt{5}\right)\left(\sqrt{5}+\sqrt{3}\right)}{5-3}$$
$$\frac{\left(2+\sqrt{5}\right)\left(\sqrt{5}+\sqrt{3}\right)}{2}$$
$$\frac{2\sqrt{5}+2\sqrt{3}+\left(\sqrt{5}\right)^{2}+\sqrt{5}\sqrt{3}}{2}$$
$$\frac{2\sqrt{5}+2\sqrt{3}+5+\sqrt{5}\sqrt{3}}{2}$$
$$\frac{2\sqrt{5}+2\sqrt{3}+5+\sqrt{15}}{2}$$
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