This is part of a question from Hungerford.
Let $K$ be a field.Let $u=f(x)/g(x) $in $K(x)-K$.Assume that $gcd(f,g)=1.$
Then,I have to show that $ug(y)-f(y) \in K(u)[y]$is irreducible in $K(u).$To show this,it is sufficient to show that it is irreducible over $K[u]$(since the polynomial is primitive).
The hint is given that it follows since $f,g$ are relatively prime and $ug(y)-f(y)$ is linear in $u$.Can someone explain this?