Discovering equations

 

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? (75 words)

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