Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: How do i prove this ?

  1. May 18, 2008 #1
    I am working my way through Serge Langs A first course in Calculus and have encountered this question/proof which i am not sure how to do. Any assistance much appreciated.

    Let a,b,c,d > 0 such that a/b > c/d Prove that

    a/b < (a+c)/(b+d)


    Last edited: May 18, 2008
  2. jcsd
  3. May 18, 2008 #2

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    IN which section is this? The surrounding material may well be helpful - is it near stuff on cauchy schwartz, or the triangle inequality? Or something else entirely? My experience with this type of question is that it is 'easy' with the right method, and impossible if you don't know/guess it. Any similar questions in the text near this one may well give you plenty of insight.
  4. May 18, 2008 #3


    User Avatar
    Science Advisor

    My first thought would be to multiply both sides of the inequality by b and b+ d.
  5. May 18, 2008 #4
    It is wrong.
    If a/b > c/d , then
    ad > bc , or
    ab+ad > ab+bc , or
    a(b+d) > b(a+c) , or
    a/b > (a+c)/(b+d)

    That's all.
  6. May 18, 2008 #5
    Thanks. Yes i got the direction of the inequality the wrong way round but i see your approach. First multiply both side by b, then d and then add ab to both sides, all of which can only be done on the assumption that all values are > 0 and hence preserving the direction of the inequality.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook