# How do i prove this ?

• dmcharg
In summary, the conversation is about solving a question/proof in Serge Lang's A first course in Calculus involving the inequality a/b > c/d and proving that a/b < (a+c)/(b+d). The suggested approach is to multiply both sides by b and b+d, and then add ab to both sides, assuming that all values are greater than 0.

#### dmcharg

Hi
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)

?

Thanks
David.

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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.

My first thought would be to multiply both sides of the inequality by b and b+ d.

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

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

It is wrong.
If a/b > c/d , then