$$\frac{x^{2}}{2}-\frac{2}{x^{2}}$$
$\frac{x^{2}}{2}-\frac{2}{x^{2}}$
$$\frac{x^{2}x^{2}}{2x^{2}}-\frac{2\times 2}{2x^{2}}$$
$$\frac{x^{2}x^{2}-2\times 2}{2x^{2}}$$
$$\frac{x^{4}-4}{2x^{2}}$$
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$\frac{\left(x^{2}-2\right)\left(x^{2}+2\right)}{2x^{2}}$
