Results 1 to 3 of 3

Math Help - field axioms proof

  1. #1
    Newbie
    Joined
    May 2007
    Posts
    2

    field axioms proof

    How do I prove that

    (a/b) - (c/d) = (ad - bc)/(bd) if b =/ 0 and d =/0

    Thank you
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by papercut06 View Post
    How do I prove that

    (a/b) - (c/d) = (ad - bc)/(bd) if b =/ 0 and d =/0

    Thank you
    you can literally combine the two fractions on the left and you will get the ones on the right. there are dozens of ways to do this, use your favorite method of subtracting fractions.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by papercut06 View Post
    How do I prove that

    (a/b) - (c/d) = (ad - bc)/(bd) if b =/ 0 and d =/0

    Thank you
    If b,d\not =0 are elements of a field then,

    a/b = ab^{-1} \mbox{ and } c/d = cd^{-1} be definition.

    Then, ad/bd = (ad)(db)^{-1} = ad^{-1}db^{-1} = a/b

    Similarly, bc/bd = c/d.

    Hence, a/b - c/d = ad/bd - bc/bd = (ad)(bd)^{-1} - (bc)(bd)^{-1} = [ad-bc](bd)^{-1} = (ad-bc)/bd
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. proof of axioms
    Posted in the Advanced Statistics Forum
    Replies: 7
    Last Post: November 10th 2010, 02:40 PM
  2. [SOLVED] Field Axioms
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: September 6th 2010, 06:03 PM
  3. Using Field Axioms
    Posted in the Advanced Algebra Forum
    Replies: 9
    Last Post: July 6th 2007, 04:14 PM
  4. Another proof using Ordered Field Axioms
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: April 7th 2007, 05:36 PM
  5. Proof using Ordered Field Axioms
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: April 7th 2007, 04:51 PM

Search Tags


/mathhelpforum @mathhelpforum