If I homogenized $f(z) = \frac{az+b}{cz+d}$, what would that look like and what would the process be to doing it?

Question

I have a quick question. If I homogenized $f(z) = \displaystyle\frac{az+b}{cz+d}$, what would that look like and what would the process be to doing it? I am extremely new to homogenization and I and self teaching this to myself. They had other examples but I got ambitious and wanted to try this one.