$$x^{2}+8+\frac{16}{x^{2}}$$
$\left(x+\frac{4}{x}\right)^{2}$
$$\frac{\left(x^{2}+8\right)x^{2}}{x^{2}}+\frac{16}{x^{2}}$$
$$\frac{\left(x^{2}+8\right)x^{2}+16}{x^{2}}$$
$$\frac{x^{4}+8x^{2}+16}{x^{2}}$$
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$\frac{\left(x^{2}+4\right)^{2}}{x^{2}}$
