1. The problem statement, all variables and given/known data Expand x/(x-1) at a=1 The book already gives the expansion but it doesn't explain the process. The expansion it gives is: x/(x-1) = (1+x-1)/(x-1) = (x-1)^(-1) + 1 2. Relevant equations 3. The attempt at a solution I've already solved for the Mclaurin expansion for the same polynomial which gives me -x - x^2 - x^3 - x^4 - ..... The derivatives all have a power of (x-1) as its denominator therefore all of its derivatives are undefined. I don't know any other way to expand polynomials other than term by term, I've been staring at x/(x-1) = (1+x-1)/(x-1) = (x-1)^(-1) + 1 But it doesn't make sense. All they did was just split the fraction up into two parts.