I'm reading through complex functions in Boas' book, and there's a part when discussing Laurent series where she says:
"Now, for $0 <|z|<1$, we expand each of the fractions in the parenthesis in powers of $z$."
The equation she refers to is the following:
$$f(z) = \frac {4}{z} \left({\frac{1}{1+z}}+ {\frac{1}{2-z}}\right).$$
As a result of the expansion, she gets:
$$f(z)=-3+9z/2-15z^2/4+33z^3/8+ \cdots +6/z.$$
I have no clue how she got the second equation from the first. Specifically, I don't know what she means by "expand each of the fractions in the parenthesis in powers of $z$". An explanation would be appreciated.