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Is this a complex analysis course, or is it something that had complex analysis as a prerequisite?
Practically, to calculate these you can often do standard Taylor series calculations
[tex]f(x)=\frac{x}{1-x} = \frac{1}{1-1/x}[/tex]
we know how to expand 1/(1-1/x) using the Taylor series for 1/(1-x)
[tex] f(x) = 1+\frac{1}{x}+\frac{1}{x^2}+\frac{1}{x^3}+...[/tex]
and this is valid as long as |x|>1
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