A problem by d w

Level pending

1. a = b 2. a 2 = a b 3. a 2 − b 2 = a b − b 2 4. ( a − b ) ( a + b ) = b ( a − b ) 5. a + b = b 6. b + b = b 7. 2 b = b 8. 2 = 1 1.\quad a=b\\ 2.\quad { a }^{ 2 }=ab\\ 3.\quad { a }^{ 2 }-{ b }^{ 2 }=ab-{ b }^{ 2 }\\ 4.\quad (a-b)(a+b)=b(a-b)\\ 5.\quad a+b=b\\ 6.\quad b+b=b\\ 7.\quad 2b=b\\ 8.\quad 2=1

Which line is the mistake found in?


The answer is 5.

D W by d w , 21, Canada

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1 solution

Zach Abueg
Jan 15, 2017

a = b a = b , so a − b = 0. a - b = 0.

To divide by ( a − b ) (a - b) on both sides at step 5 5 is to divide by 0 0 , which is undefined.

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