Solving the Multivariable Proof: A+C/B+D < E+G/F+H

[Fenix]

I'm confronted with the following question that may of may not have a solution:

You are given eight variables, A, B, C, D, E, F, G, and H.

These variables are integers.

You know that:

A/B > E/F

and

C/D > G/H

Is it possible that (A+C)/(B+D) < (E+G)/(F+H)?

I've tried everything, such as multiplying, and expanding, but that did not get me anywhere. I also tried trial and error with unsuccessful results.

Is it even possible?

 

[vincentchan]

how about C=D=10000000000, G=1,H=2,A=1000,B=1,E=500,F=1

 

[Fenix]

That's so astronomically huge!

I was thinking about it, and found another solution:

A=1
B=2
C=1
D=2
E=-200
F=50
G=150
H=-100

1/2 < -50/-50 = 1

Now that we found some variables that solved the existence of the question, how can we begin to apporach at deriving the parameters of the variables that will satisfy A+C/B+D < E+G/F+H?