$$\frac{1}{4\sqrt{2}}(1+\sqrt{3})-\frac{1}{4\sqrt{2}}(1+\sqrt{3})$$
$0$
$$\frac{\sqrt{2}}{4\left(\sqrt{2}\right)^{2}}\left(1+\sqrt{3}\right)-\frac{1}{4\sqrt{2}}\left(1+\sqrt{3}\right)$$
$$\frac{\sqrt{2}}{4\times 2}\left(1+\sqrt{3}\right)-\frac{1}{4\sqrt{2}}\left(1+\sqrt{3}\right)$$
$$\frac{\sqrt{2}}{8}\left(1+\sqrt{3}\right)-\frac{1}{4\sqrt{2}}\left(1+\sqrt{3}\right)$$
$$\frac{\sqrt{2}\left(1+\sqrt{3}\right)}{8}-\frac{1}{4\sqrt{2}}\left(1+\sqrt{3}\right)$$
$$\frac{\sqrt{2}\left(1+\sqrt{3}\right)}{8}-\frac{\sqrt{2}}{4\left(\sqrt{2}\right)^{2}}\left(1+\sqrt{3}\right)$$
$$\frac{\sqrt{2}\left(1+\sqrt{3}\right)}{8}-\frac{\sqrt{2}}{4\times 2}\left(1+\sqrt{3}\right)$$
$$\frac{\sqrt{2}\left(1+\sqrt{3}\right)}{8}-\frac{\sqrt{2}}{8}\left(1+\sqrt{3}\right)$$
$$\frac{\sqrt{2}\left(1+\sqrt{3}\right)}{8}-\frac{\sqrt{2}\left(1+\sqrt{3}\right)}{8}$$
$$\frac{\sqrt{2}\left(1+\sqrt{3}\right)}{8}-\frac{\sqrt{2}+\sqrt{2}\sqrt{3}}{8}$$
$$\frac{\sqrt{2}\left(1+\sqrt{3}\right)}{8}-\frac{\sqrt{2}+\sqrt{6}}{8}$$
$$\frac{\sqrt{2}\left(1+\sqrt{3}\right)-\left(\sqrt{2}+\sqrt{6}\right)}{8}$$
$$\frac{\sqrt{2}+\sqrt{6}-\sqrt{2}-\sqrt{6}}{8}$$
$$\frac{0}{8}$$
$$0$$
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