Question

to subtract c/d from a/b,we add the additive inverse of a/b to c/d

Answer 1

(a/b to c/d)=a+b-c+d

Answer 2

No.
What you want to do is subtract c/d from a/b for which you need to add the additive inverse of c/d to a/b

a/b + (-c/d) = a/b - c/d.

What you suggested was...
c/d + (-a/b) = c/d - a/b. Which is incorrect for the given question.