Expert: Paul Klarreich - 9/8/2009

Question
what is wrong in this problem (all the rules are followed according to the rules of equality)

         a=1  and  b=1
therefore a=b
so,       a²= ab

         a²-b²=ab-b²  and when factored:
       (a+b)(a-b)= b(a-b)    then
              a+b=b       so, since a=1 and b=1    
              1+1=1      BUT 1+1≠1 and ALL the rules of equality were followed so what is wrong??
Please help me solve this since it will really help my grade go up if you help me solve it and thankyou!

Answer
Questioner: Lorena
Country: United States
Category: Advanced Math
Private: Yes
Subject: Rules of Equality
Question: what is wrong in this problem (all the rules are followed according to the rules of equality)

        a=1  and  b=1
therefore a=b
so,       a²= ab

        a²-b²=ab-b²  and when factored:
      (a+b)(a-b)= b(a-b)    then
             a+b=b       so, since a=1 and b=1    
             1+1=1      BUT 1+1≠1 and ALL the rules of equality were followed so what is wrong??
Please help me solve this since it will really help my grade go up if you help me solve it and thankyou!
..............................................
Please!! This one is as old as the hills.

Look up MATHEMATICAL FALLACIES -- DIVISION BY ZERO.

That is the clue.  (Isn't  a-b = 0?)