The final question on my alg2 exam last year.

[RainGame53]

1. Let a and b be equal non-zero quantities

a = b


2. Multiply through by a

a^2 = ab


3. Subtract b^2

a^2 − b^2 = ab − b^2


4. Factor both sides

(a − b)(a + b) = b(a − b)


5. Divide out (a − b)

a + b = b


6. Observing that a = b

b + b = b


7. Combine like terms on the left

2b = b


8. Divide by b

2 = 1


We had to write what causes the false answer and why. What a weird problem.