$$\frac{6-4\sqrt{3}}{6+4\sqrt{3}}$$
$4\sqrt{3}-7\approx -0.07179677$
$$\frac{\left(6-4\sqrt{3}\right)\left(6-4\sqrt{3}\right)}{\left(6+4\sqrt{3}\right)\left(6-4\sqrt{3}\right)}$$
$$\frac{\left(6-4\sqrt{3}\right)\left(6-4\sqrt{3}\right)}{6^{2}-\left(4\sqrt{3}\right)^{2}}$$
$$\frac{\left(6-4\sqrt{3}\right)^{2}}{6^{2}-\left(4\sqrt{3}\right)^{2}}$$
$$\frac{36-48\sqrt{3}+16\left(\sqrt{3}\right)^{2}}{6^{2}-\left(4\sqrt{3}\right)^{2}}$$
$$\frac{36-48\sqrt{3}+16\times 3}{6^{2}-\left(4\sqrt{3}\right)^{2}}$$
$$\frac{36-48\sqrt{3}+48}{6^{2}-\left(4\sqrt{3}\right)^{2}}$$
$$\frac{84-48\sqrt{3}}{6^{2}-\left(4\sqrt{3}\right)^{2}}$$
$$\frac{84-48\sqrt{3}}{36-\left(4\sqrt{3}\right)^{2}}$$
$$\frac{84-48\sqrt{3}}{36-4^{2}\left(\sqrt{3}\right)^{2}}$$
$$\frac{84-48\sqrt{3}}{36-16\left(\sqrt{3}\right)^{2}}$$
$$\frac{84-48\sqrt{3}}{36-16\times 3}$$
$$\frac{84-48\sqrt{3}}{36-48}$$
$$\frac{84-48\sqrt{3}}{-12}$$
$$-7+4\sqrt{3}$$
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$-\left(7-4\sqrt{3}\right)$
