$$x+3x+2 \div x+2$$
$4x+2+\frac{2}{x}$
$$4x+\frac{2}{x}+2$$
$$\frac{\left(4x+2\right)x}{x}+\frac{2}{x}$$
$$\frac{\left(4x+2\right)x+2}{x}$$
$$\frac{4x^{2}+2x+2}{x}$$
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$\frac{2\left(2x^{2}+x+1\right)}{x}$
