$$a^{6}+\frac{1}{a^{6}}+2$$
$\frac{\left(a^{6}+1\right)^{2}}{a^{6}}$
$$\frac{\left(a^{6}+2\right)a^{6}}{a^{6}}+\frac{1}{a^{6}}$$
$$\frac{\left(a^{6}+2\right)a^{6}+1}{a^{6}}$$
$$\frac{a^{12}+2a^{6}+1}{a^{6}}$$
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$\frac{\left(a^{2}+1\right)^{2}\left(a^{4}-a^{2}+1\right)^{2}}{a^{6}}$
