How do you subtract rational expressions without a common denominator?

You would have to make common denominators
consider a/b,c/d in Q
then a/b - c/d = ad/db - cb/bd = (ad-cb)/db for all a,b,c,d in R, exclude b,d=0
i.e. 1/2 - 1/4
=4/8 - 2/8 =(4-2)/8=2/8 =1/4