Sure. What you've got there are really two inequalities that are logically AND'ed together. That is you're solving the following simultaneous inequalities:
AND
Can you write up a specific example to work on?
Once you have the problem reduced to , where a, b, c, and d are polynomials, you need to realize that "<" can change to ">" only where (1) they are "=" or (2) where at least one of the denominators is 0.
So: first solve the equation as well as b= 0 and d= 0. Those point separate "<" from ">". You can choose one point in each interval to see whether "<" or ">" is correct in that interval.
Another way is to rewrite the problem as , and then factor ac- bd as well as bd. For each interval between zeros of ac- bd, b, and d, you can count the number of negative factors to see if "> 0 " or "< 0" is correct.