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September 4th, 2014, 03:18 PM  #1 
Member Joined: Jun 2014 From: Alberta Posts: 56 Thanks: 2  Basic Algebraic Proof
Is there anything wrong with this algebraic proof? Please give a rigorous critique. Proof that a/b/(c/d) = ad/(bc) if b, c, d don't equal 0: a/b/(c/d) = a/b(c/d)^(1) [existence of multiplicative inverses] = a/b(cd^(1))^(1) = a/bc^(1)(d^(1))^(1) [Does the operation made in this step comply with a prior question that had us prove (ab)^(1) = a^(1)b^(1)?] = a/b(1/c)1/(d^(1))d/d = a/b(1/c)d = a/bd/c = ad/(bc) The reason why I posted this is because the book's answer has pretty much the same thing except that it brings b up as b^(1) and then brings it back down at the end. I feel like I am missing something here. 

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algebraic, basic, proof 
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