Let $P$ and $Q$ be real monic polynomials without common roots on $\Bbb{C}\cup\{\infty\}$ with degree $n$ and $m$ ($m>n$) respectively and only simple roots. The ramification points of $f = P^m/Q^n$ are at the roots of $f'(z) = 0$. These are at the roots of $P$, $Q$ and $mP'Q-nQ'P$.
Is it true that the only ramification point $r$ of $f$ with $f(r) = 1$ is at $\infty$?
I have found that the answer is no. A counterexample is given by $P(z) = z-1$ and $Q(z) = (z - 2) (z - 3) (z - 7 + 4 \sqrt{2})$