$$\frac{ 7+3 \sqrt{ 5 } }{ 3+ \sqrt{ 5 } }$$
$\frac{\sqrt{5}+3}{2}\approx 2.618033989$
$$\frac{\left(7+3\sqrt{5}\right)\left(3-\sqrt{5}\right)}{\left(3+\sqrt{5}\right)\left(3-\sqrt{5}\right)}$$
$$\frac{\left(7+3\sqrt{5}\right)\left(3-\sqrt{5}\right)}{3^{2}-\left(\sqrt{5}\right)^{2}}$$
$$\frac{\left(7+3\sqrt{5}\right)\left(3-\sqrt{5}\right)}{9-5}$$
$$\frac{\left(7+3\sqrt{5}\right)\left(3-\sqrt{5}\right)}{4}$$
$$\frac{21-7\sqrt{5}+9\sqrt{5}-3\left(\sqrt{5}\right)^{2}}{4}$$
$$\frac{21+2\sqrt{5}-3\left(\sqrt{5}\right)^{2}}{4}$$
$$\frac{21+2\sqrt{5}-3\times 5}{4}$$
$$\frac{21+2\sqrt{5}-15}{4}$$
$$\frac{6+2\sqrt{5}}{4}$$
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