$$=\frac{\sqrt{3}-1}{\sqrt{3}+1}$$
$2-\sqrt{3}\approx 0.267949192$
$$\frac{\left(\sqrt{3}-1\right)\left(\sqrt{3}-1\right)}{\left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right)}$$
$$\frac{\left(\sqrt{3}-1\right)\left(\sqrt{3}-1\right)}{\left(\sqrt{3}\right)^{2}-1^{2}}$$
$$\frac{\left(\sqrt{3}-1\right)\left(\sqrt{3}-1\right)}{3-1}$$
$$\frac{\left(\sqrt{3}-1\right)\left(\sqrt{3}-1\right)}{2}$$
$$\frac{\left(\sqrt{3}-1\right)^{2}}{2}$$
$$\frac{\left(\sqrt{3}\right)^{2}-2\sqrt{3}+1}{2}$$
$$\frac{3-2\sqrt{3}+1}{2}$$
$$\frac{4-2\sqrt{3}}{2}$$
$$2-\sqrt{3}$$
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