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Math Help - Please explain...proof

  1. #1
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    Please explain...proof

    Problem: Prove the following,

     \frac{a}{b} + \frac{c}{d} = \frac{ad +bc}{bd} if b,d \not= 0

    I'm sorry to say I analyze this utterly elementary proof to the point of being unable to move.

    Proof from book:  (ad + bc)/(bd) = (ad+bc)(bd)^{-1}
    (ad + bc)(bd)^{-1} by (iii) =  ab^{-1} + cd^{-1} = \frac {a}{d} + \frac{c}{d}

    the book then cites the following proof as justification for the latter equivalence:

    (iii) = (ab)^{-1} = a^{-1}b^{-1} if a,b \not= 0
    proof of (iii) from book,  ab(a^{-1}b^{-1}) = (a * a^{-1})(b * b^{-1}) = 1, so a^{-1} * b^{-1} = (ab)^{-1}




    I get that  (a)^{-1} = \frac{1}{a}
    I also understand that  bd(bd)^{-1} = 1

    There is a continuity gap in my comprehension, educate me please.
    Last edited by Foxlion; March 11th 2011 at 07:20 PM.
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  2. #2
    Master Of Puppets
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     \displaystyle \frac{a}{b} \times \frac{d}{d}+ \frac{c}{d}\times \frac{b}{b}= \dots
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  3. #3
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    There is a continuity gap in my comprehension, educate me please.
    I am not sure which step of the proof from the book is not clear to you.
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