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MathNet 2014 Question 87

Math Olympiad Vault · MathNet 2014

Question 87

Let $n$ be a positive integer. Simplify
$$\left(\frac{a+a^{-1}b^2}{a-a^{-1}b^2}-1\right)^{-1}\left(b^n(a-b)^{-1}-b^n(a+b)^{-1}\right).$$
For which values of $a,b$ is the expression undefined?