Find all possible Taylor and Laurent series expansions for the function(2z + 3)/((z + 1)(z + 2)) around z = 1 and specify the domain of validity.
Question
Solution 1
The function can be written as a partial fraction:
(2z + 3)/((z + 1)(z + 2)) = A/(z + 1) + B/(z + 2)
Solving for A and B gives A = -1 and B = 3. So the function can be rewritten as:
-1/(z + 1) + 3/(z + 2)
Now, we can find the Taylor series expansion around z = 1 for each term separately.
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