1. The problem statement, all variables and given/known data The problem comes from Lang's Basic Mathematics, chapter 1, paragraph 6 (multiplicative inverses) and simply asks to prove the relation: (xn - 1) / (x - 1) = xn - 1 + xn - 2 + ... + x + 1 2. Relevant equations a-1a = aa-1 = 1 Cross-multiplication rule Cancellation law for multiplication 3. The attempt at a solution The solution is actually given at the back of the book, but there's a couple of simplifications I have trouble understanding: (x - 1) (xn-1 + xn-2 + ... + x + 1) = x(xn-1 + xn-2 + ... + x + 1) - (xn-1 + xn-2 + ... + x + 1) = xn + xn-1 + ... + x - xn-1 - xn-2 - ... - x - 1 = xn - 1 The two things I don't understand are: Shouldn't the result of x(xn-1 + xn-2 + ... + x + 1) include x2? [line 2] How is xn-2 excluded from the final result? [line 3] Thanks in advance for your help!