Question

Find the error in the following proof that 2 = 1. Consider the equation a = b. Multiply both sides by a to obtain a 2 = ab. Subtract b 2 from both sides to get a 2 − b 2 = ab − b 2 . Now factor each side, (a + b)(a − b) = b(a − b), and divide each side by (a − b) to get a + b = b. Finally, let a and b equal 1, which shows that 2 = 1.

Answer 1

You can't divide by zero

Step-by-step explanation:

The error appears when you divide each side by (a - b). If a = b, then (a - b) = 0 and you can't divide each side by 0. Moreover, the equation before division, that is, (a + b)(a − b) = b(a − b) is true after replacing (a - b) = 0 because it gives 0 = 0.