Proving non-existence of poles of differential 1-form on zero set in $\mathbb{A}^2$

Question

For the differential 1-form $\omega_0=\frac{dx}{ny^{n-1}}=\frac{dy}{(n-1)x^{n-2}}$ ($n\in\mathbb{Z}_{\geqslant2}$ and $n(n-1)\in k^*$) I want to show that it doesn't have any poles on $U=Z(f)\subset\mathbb{A}^2$ where $f=x^{n-1}-y^n-1$. Now I guess that the poles are the points $(x,y)\in\mathbb{A}^2$ where either $ny^{n-1}=0$ or $(n-1)x^{n-2}=0$. By this definition there is a pole $(x,y)=(1,0)$, but there shouldn't be any, so certainly I am doing something wrong and the question is: how to fix that?