A missing term and a cubic coefficient

A missing term and a cubic coefficient

IB Year 5 | Grade 11
5 marks

The coefficient of \(x^2\) in \((1+ax)(1+x)^{-2}\) is zero. Find \(a\), then find the coefficient of \(x^3\) and the open range of validity.[5]

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Answer:\(a=\frac32;\ \frac12;\ |x|<1\)

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