Hi Bober, thanks for your patience.

There is indeed something missing in there. We should have $$x^2\left(x^2 + 2 + \dfrac{1}{x^2} + 7x  + \dfrac{7}{x} + 12\right).$$

Since $\left(x + \dfrac{1}{x}\right)^2 = x^2 + 2 + \frac{1}{x^2}$, we now have that the expression is equal to $x^2(y^2 + 7y + 12)$