If ab is not equal to 0, what is the absolute value of a + b + ab?

If ab is not equal to 0, what is the absolute value of a + b + ab?

A >0, b >0:
Original formula=1+1+1=3
A <0, b <0:
Original formula=-1-1+1=-1
A >0, b <0;
Original formula=1-1-1=-1
A <0,b>0:
Original formula=-1+1-1=-1

It is proved that the product of irrational number and rational number is irrational number. Prove that the product of irrational number and rational number is irrational number.

Counter evidence method
Let a be a rational number and b be an irrational number
Suppose ab is a rational number, then b=ab/a, because ab and a are both rational numbers, and the quotient of two rational numbers is also a rational number, so b is a rational number, which contradicts b is an irrational number
So it's not true.
So ab is irrational

Counter evidence
Let a be a rational number and b be an irrational number
Suppose ab is a rational number, then b=ab/a, because ab and a are both rational numbers, the quotient of two rational numbers is also a rational number, so b is a rational number, which is contradictory to b is an irrational number
So it's not true.
So ab is irrational

Counter evidence law
Let a be a rational number and b be an irrational number
Suppose ab is a rational number, then b=ab/a, because ab and a are both rational numbers, and the quotient of two rational numbers is also a rational number, so b is a rational number, which contradicts b is an irrational number
So it's not true.
So ab is irrational