Binomial Expansion

For what values of x can the function \displaystyle \frac{5x-3}{\left(x-1\right)^{2}\left(x+1\right)} be expanded as a power series in x?  If n is even, prove that the coefficient of x^n is n-3.

Source: Porter, R.I. (1963). Further Elementary Analysis (2nd ed.). London: G. Bell & Sons. (Miscellaneous Examples, Question 8, p. 221)

Author: ascklee

Dr. Lee teaches at the Wee Kim Wee School of Communication and Information at the Nanyang Technological University in Singapore. He founded The Mathematics Digital Library in 2013.

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