If ab is a nonzero rational number, find all possible values of the absolute value of a + b

If ab is a nonzero rational number, find all possible values of the absolute value of a + b

Three categories
1.A, b are both positive
A/|a b/|b|=1+1=2
2.A, b are both negative
A/|a b/|b =-1-1=-2
3.A, b different sign
A/|a b/|b|=0

If A·B is a non-zero rational number, discuss all possible values of expression: a/|a b/|b ab/|ab| 1 If a and b are nonzero rational numbers, discuss all possible values of the formula: a/|a b/|b ab/|ab| 2. If A·B is a nonzero rational number, discuss all possible values of the formula: a/|a b/|b ab/|ab| 1 If a and b are nonzero rational numbers, discuss all possible values of the formula: a/|a b/|b ab/|ab| 2.

Discussion by case:
1, A >0, B >0
A/|a b/|b ab/|ab|=1+1+1=3
2, A >0, B