$$\frac{ 5+2 \sqrt{ 6 } -1 }{ 5+2 \sqrt{ 6 } -3 }$$
$\frac{\sqrt{6}+4}{5}\approx 1.289897949$
$$\frac{4+2\sqrt{6}}{5+2\sqrt{6}-3}$$
$$\frac{4+2\sqrt{6}}{2+2\sqrt{6}}$$
$$\frac{\left(4+2\sqrt{6}\right)\left(2-2\sqrt{6}\right)}{\left(2+2\sqrt{6}\right)\left(2-2\sqrt{6}\right)}$$
$$\frac{\left(4+2\sqrt{6}\right)\left(2-2\sqrt{6}\right)}{2^{2}-\left(2\sqrt{6}\right)^{2}}$$
$$\frac{\left(4+2\sqrt{6}\right)\left(2-2\sqrt{6}\right)}{4-\left(2\sqrt{6}\right)^{2}}$$
$$\frac{\left(4+2\sqrt{6}\right)\left(2-2\sqrt{6}\right)}{4-2^{2}\left(\sqrt{6}\right)^{2}}$$
$$\frac{\left(4+2\sqrt{6}\right)\left(2-2\sqrt{6}\right)}{4-4\left(\sqrt{6}\right)^{2}}$$
$$\frac{\left(4+2\sqrt{6}\right)\left(2-2\sqrt{6}\right)}{4-4\times 6}$$
$$\frac{\left(4+2\sqrt{6}\right)\left(2-2\sqrt{6}\right)}{4-24}$$
$$\frac{\left(4+2\sqrt{6}\right)\left(2-2\sqrt{6}\right)}{-20}$$
$$\frac{8-8\sqrt{6}+4\sqrt{6}-4\left(\sqrt{6}\right)^{2}}{-20}$$
$$\frac{8-4\sqrt{6}-4\left(\sqrt{6}\right)^{2}}{-20}$$
$$\frac{8-4\sqrt{6}-4\times 6}{-20}$$
$$\frac{8-4\sqrt{6}-24}{-20}$$
$$\frac{-16-4\sqrt{6}}{-20}$$
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