The rule for multplying and dividing both sides of an inequality do not meantion zero. Explain why??

Answer 1

In general, we do not multiply or divide each side of an equality by zero, as it could give erroneous results. So the same applies to inequalities.

For example:
A=B
Multiply by A:
A*A = A*B
Subtract B²:
A²-B² = AB - B²
Factor each side:
(A+B)(A-B) = B(A-B)
Cancel out (A-B)
A+B = B

How does the fallacy work: we divided each side by (A-B) which is zero!