$$\frac{7+\sqrt{3}}{7-\sqrt{3}}$$
$\frac{7\sqrt{3}+26}{23}\approx 1.657580681$
$$\frac{\left(7+\sqrt{3}\right)\left(7+\sqrt{3}\right)}{\left(7-\sqrt{3}\right)\left(7+\sqrt{3}\right)}$$
$$\frac{\left(7+\sqrt{3}\right)\left(7+\sqrt{3}\right)}{7^{2}-\left(\sqrt{3}\right)^{2}}$$
$$\frac{\left(7+\sqrt{3}\right)\left(7+\sqrt{3}\right)}{49-3}$$
$$\frac{\left(7+\sqrt{3}\right)\left(7+\sqrt{3}\right)}{46}$$
$$\frac{\left(7+\sqrt{3}\right)^{2}}{46}$$
$$\frac{49+14\sqrt{3}+\left(\sqrt{3}\right)^{2}}{46}$$
$$\frac{49+14\sqrt{3}+3}{46}$$
$$\frac{52+14\sqrt{3}}{46}$$
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