$$\frac { 6 - 4 \sqrt { 2 } } { 6 + 4 \sqrt { 2 } }$$
$17-12\sqrt{2}\approx 0.029437252$
$$\frac{\left(6-4\sqrt{2}\right)\left(6-4\sqrt{2}\right)}{\left(6+4\sqrt{2}\right)\left(6-4\sqrt{2}\right)}$$
$$\frac{\left(6-4\sqrt{2}\right)\left(6-4\sqrt{2}\right)}{6^{2}-\left(4\sqrt{2}\right)^{2}}$$
$$\frac{\left(6-4\sqrt{2}\right)^{2}}{6^{2}-\left(4\sqrt{2}\right)^{2}}$$
$$\frac{36-48\sqrt{2}+16\left(\sqrt{2}\right)^{2}}{6^{2}-\left(4\sqrt{2}\right)^{2}}$$
$$\frac{36-48\sqrt{2}+16\times 2}{6^{2}-\left(4\sqrt{2}\right)^{2}}$$
$$\frac{36-48\sqrt{2}+32}{6^{2}-\left(4\sqrt{2}\right)^{2}}$$
$$\frac{68-48\sqrt{2}}{6^{2}-\left(4\sqrt{2}\right)^{2}}$$
$$\frac{68-48\sqrt{2}}{36-\left(4\sqrt{2}\right)^{2}}$$
$$\frac{68-48\sqrt{2}}{36-4^{2}\left(\sqrt{2}\right)^{2}}$$
$$\frac{68-48\sqrt{2}}{36-16\left(\sqrt{2}\right)^{2}}$$
$$\frac{68-48\sqrt{2}}{36-16\times 2}$$
$$\frac{68-48\sqrt{2}}{36-32}$$
$$\frac{68-48\sqrt{2}}{4}$$
$$17-12\sqrt{2}$$
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$17-12\sqrt{2}$
