Question

Suppose a,b,c, and d are positive numbers such that a/b < c/d. Show that:

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

NOTE: PLEASE DO NOT WRITE OUT THE SOLUTION! I would like a hint as to how I should approach this. OR, if there is any concept I should look up to aid me with finding the answer for this question, please do share.

Thanks in advance

Answer 1

\[\frac{a}{b} < \frac{c}{d} \iff ad < bc \iff ad-bc < 0 \]
from here you want to add and subtract something so you can factor. You will need to do it twice with 2 different things to finish the problem completely.
I hope this doesnt give too much away, i couldnt think of another way to say it unfortunately.