Suppose a and b are equal and are an arbitrary number
Given: a = b
Multiply both sides by a
a2 = ab
Subtract b2 from both sides
a2 - b2 = ab - b2
Factor
(a + b)(a - b) = b(a - b)
Divide both sides by (a - b)
a + b = b
Substitue b for a, since they're equal (from the given)
b + b = b
Divide both sides by b
1 + 1 = 1
Add
2 = 1
Q.E.D.
Answer (highlight):
| a and b are equal, so when you divided both sides by (a - b) you were actually dividing by 0...which is bad. Weird things like this happen. |
Come back next week when I show you how to do your taxes in a similar fashion!