Expert: Paul Klarreich - 10/28/2005

Question
a=b

multiply both sides by a
a^2 = ab

add a^2-2ab to both sides
a^2+ a^2-2ab = ab+a^2 -2ab

simplify
2(a^2-ab) = a^2 -ab

divide by a^2-ab
2=1

How come?  (note ^ means squared or to the power of)

Answer
Hi, Sommer,

GIMME A BREAK!  This is one of the old chestnuts.  You will REALLY find out what happened when you begin to study calculus and find out why the graph of y = (x^ - 2x)/x  is not the same as the graph of   y = x - 2

Or why the equation  x = 2  is not equivalent to the equation x^2 = 2x.


Try your so-called proof over again, but this time, do it the way you did your geometry proofs:

Left column:                 Right column:
Statement                    Reason.

Where the reason is some clearly stated rule, not omitting important detail, for which the statement is an example.

a=b

1. multiply both sides by a
a^2 = ab   (STATE YOUR REASON FOR THIS)

2. add a^2-2ab to both sides
a^2+ a^2-2ab = ab+a^2 -2ab  (STATE YOUR REASON FOR THIS)

simplify
3. 2(a^2-ab) = a^2 -ab (STATE YOUR REASON FOR THIS)


4. divide by a^2-ab (STATE YOUR REASON FOR THIS)
2=1

Guess what?  You won't be able to state a clear-cut reason for step 4.