Find a power series for the function: f(x) = 1+x/1-x so the solution shows: f(x) = -1 + 2/1-x >>>>>>what happened to the +x in the numerator at this point? -1+ 2 series sign x^n
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When you do long division, the x gets divided by x somewhere, and x/x = 1 (1+x) / (1-x) gives -1, and a remainder of 2, hence, $\displaystyle \dfrac{1+x}{1-x} = -1 + \dfrac{2}{1-x}$
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