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September 4th, 2014, 03:18 PM   #1
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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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