$$\frac { 6 \sqrt { 3 } } { 2 - \sin 45 }$$
$\frac{6\sqrt{3}\left(\sqrt{2}+4\right)}{7}\approx 8.038022548$
$$\frac{6\sqrt{3}}{2-\frac{\sqrt{2}}{2}}$$
$$\frac{6\sqrt{3}}{\frac{2\times 2}{2}-\frac{\sqrt{2}}{2}}$$
$$\frac{6\sqrt{3}}{\frac{2\times 2-\sqrt{2}}{2}}$$
$$\frac{6\sqrt{3}}{\frac{4-\sqrt{2}}{2}}$$
$$\frac{6\sqrt{3}\times 2}{4-\sqrt{2}}$$
$$\frac{6\sqrt{3}\times 2\left(4+\sqrt{2}\right)}{\left(4-\sqrt{2}\right)\left(4+\sqrt{2}\right)}$$
$$\frac{6\sqrt{3}\times 2\left(4+\sqrt{2}\right)}{4^{2}-\left(\sqrt{2}\right)^{2}}$$
$$\frac{6\sqrt{3}\times 2\left(4+\sqrt{2}\right)}{16-2}$$
$$\frac{6\sqrt{3}\times 2\left(4+\sqrt{2}\right)}{14}$$
$$\frac{12\sqrt{3}\left(4+\sqrt{2}\right)}{14}$$
$$\frac{6}{7}\sqrt{3}\left(4+\sqrt{2}\right)$$
$$\frac{24}{7}\sqrt{3}+\frac{6}{7}\sqrt{3}\sqrt{2}$$
$$\frac{24}{7}\sqrt{3}+\frac{6}{7}\sqrt{6}$$
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