# What is the limit of ((2-x)^2(3-x)^2(1-x)) / (2-x^2)^2 as x goes to infinity?

The numerator has leading term $- {x}^{5}$, the denominator has leading term ${x}^{4}$.
The terms other than the leading term do not matter for $x \rightarrow \infty$, so
${\lim}_{x \rightarrow \infty} \frac{{\left(2 - x\right)}^{2} {\left(3 - x\right)}^{2} \left(1 - x\right)}{2 - {x}^{2}} ^ 2 = - \infty$