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