$$\frac{5-2\sqrt{6}}{5+2\sqrt{6}}$$
$49-20\sqrt{6}\approx 0.010205144$
$$\frac{\left(5-2\sqrt{6}\right)\left(5-2\sqrt{6}\right)}{\left(5+2\sqrt{6}\right)\left(5-2\sqrt{6}\right)}$$
$$\frac{\left(5-2\sqrt{6}\right)\left(5-2\sqrt{6}\right)}{5^{2}-\left(2\sqrt{6}\right)^{2}}$$
$$\frac{\left(5-2\sqrt{6}\right)^{2}}{5^{2}-\left(2\sqrt{6}\right)^{2}}$$
$$\frac{25-20\sqrt{6}+4\left(\sqrt{6}\right)^{2}}{5^{2}-\left(2\sqrt{6}\right)^{2}}$$
$$\frac{25-20\sqrt{6}+4\times 6}{5^{2}-\left(2\sqrt{6}\right)^{2}}$$
$$\frac{25-20\sqrt{6}+24}{5^{2}-\left(2\sqrt{6}\right)^{2}}$$
$$\frac{49-20\sqrt{6}}{5^{2}-\left(2\sqrt{6}\right)^{2}}$$
$$\frac{49-20\sqrt{6}}{25-\left(2\sqrt{6}\right)^{2}}$$
$$\frac{49-20\sqrt{6}}{25-2^{2}\left(\sqrt{6}\right)^{2}}$$
$$\frac{49-20\sqrt{6}}{25-4\left(\sqrt{6}\right)^{2}}$$
$$\frac{49-20\sqrt{6}}{25-4\times 6}$$
$$\frac{49-20\sqrt{6}}{25-24}$$
$$\frac{49-20\sqrt{6}}{1}$$
$$49-20\sqrt{6}$$
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