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

  • Math -

    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:
    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!

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