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