$$\frac{ \sqrt{ 2 } }{ \sqrt{ 2 } + \sqrt{ 3 } } \times \frac{ \sqrt{ 2 } - \sqrt{ 3 } }{ \sqrt{ 2 } - \sqrt{ 3 } }$$
$\sqrt{6}-2\approx 0.449489743$
$$\frac{\sqrt{2}}{\sqrt{2}+\sqrt{3}}\times 1$$
$$\frac{\sqrt{2}\left(\sqrt{2}-\sqrt{3}\right)}{\left(\sqrt{2}+\sqrt{3}\right)\left(\sqrt{2}-\sqrt{3}\right)}\times 1$$
$$\frac{\sqrt{2}\left(\sqrt{2}-\sqrt{3}\right)}{\left(\sqrt{2}\right)^{2}-\left(\sqrt{3}\right)^{2}}\times 1$$
$$\frac{\sqrt{2}\left(\sqrt{2}-\sqrt{3}\right)}{2-3}\times 1$$
$$\frac{\sqrt{2}\left(\sqrt{2}-\sqrt{3}\right)}{-1}\times 1$$
$$\left(-\sqrt{2}\left(\sqrt{2}-\sqrt{3}\right)\right)\times 1$$
$$\left(-\left(\left(\sqrt{2}\right)^{2}-\sqrt{2}\sqrt{3}\right)\right)\times 1$$
$$\left(-\left(2-\sqrt{2}\sqrt{3}\right)\right)\times 1$$
$$\left(-\left(2-\sqrt{6}\right)\right)\times 1$$
$$\left(-2-\left(-\sqrt{6}\right)\right)\times 1$$
$$\left(-2+\sqrt{6}\right)\times 1$$
$$-2+\sqrt{6}$$
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