Find the Laurent series for $f(z)=\frac{2z-3}{z^2-3z+2}$ centered in the origin and convergent in the point $z=\frac32$, specifying it's convergence domain.
So I'm having troubles understanding what the problem means with "convergent in the point $z=\frac32$", usually the problems of this type ask me to find the series of a function in a range such as $|z|<1$ and centered at a point, but I don't know which range I am asked for here.
On any case I know $z=1,z=2$ are the two ceros of the function, and to find the Laurent series I would need to separate in 2 functions by doing partial fractions: $$\frac{2z-3}{z^2-3z+2}=\frac{1}{z-1}+\frac{1}{z-2}$$ but again my doubt is what they mean by that "convergent in the point $z=\frac32$", and hence how am I supposed to know the convergence domain