I'm a bit confused regarding the following example: it is stated that $$ \frac{x^3+y^3+z^3}{x^2yz}$$ is a meromorphic section of $\mathcal{O}_{\mathbb{P}^2}(-1)$, and then one is asked to find poles and zeros.
Passing in a patch where $x \neq 0$ we can multiply by $x$ and write $$ \frac{1+w_1^3+w_2^3}{w_1w_2}$$ but this doesn't have a limit for $(w_1,w_2) \to (-1,0)$: how does this fact (if correct) rely with the above?