# Math Help - Laurent series question

1. ## Laurent series question

find the laurent series of $f(x)=\frac{-2}{z-1}$+ $\frac{3}{z+2}$
for
1<|z|<2
i was by my teacher that the radius of convergence
is what smaller then the number which makes the denominator 0.
if
$f(x)=\frac{1}{1-z}$
then
the radius is 1 and
because 1-1=0
so
it is analitical on
|z|<1
so if i apply the same logic
$f(x)=\frac{-2}{z-1}$

1 still makes denominator 0
and
it is analitical on
|z|<1
but the correct answer is
it is analitical on
|z|>1
for
$f(x)=\frac{3}{z+2}$
-2 makes denominator 0
so |z|<-2 (but its illogical because |z| is a positive numbe)
where is my mistake?