$$x+1 \div { x }^{ 2 } -x+1$$
$1+\frac{1}{x^{2}}$
$$\frac{1}{x^{2}}+1$$
$$\frac{1}{x^{2}}+\frac{x^{2}}{x^{2}}$$
$$\frac{1+x^{2}}{x^{2}}$$
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$\frac{x^{2}+1}{x^{2}}$