Let $P(s)$, $Q(s)$, $A(s)$, and $B(s)$ be polynomials of a complex variable such that $P(s)/Q(s)=A(s)/B(s)$.
The polynomials have degree as follows: degree $P(s)\le n$, degree $Q(s)=n$, degree $A(s) \le r$, degree $B(s) = r$, and $n>r$.
Why does this imply that the polynomials are not coprime?
This last fact is stated in a textbook with no explanation as to why. For context, this is a proof in control theory regarding controllability of LTI system in the Laplace domain.