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