Consider the equation (x – 1)(x + 2) = 5(x – 1). First, solve this equation by dividing each side of the equation by x-1. Second, solve the equation by first “FOIL”ing the left side, then simplifying by bring all terms to the left side of the equation, and then finally solve using factoring. Why are the solutions to these two methods different?
Solving using the first method, you get x=3. Using the second method, you get x=1, 3. The reason you cannot divide of the factors is because you are assuming that (x-1) ≠ 0. If x=1 then the term = 0 and you cannot do a zero division.