One equal two

Consider two numbers A and B equal:

    A = B
    so
    A² = B²
    A² - B² = A² - B²
    (A + B) (A - B) = A² - B²
    therefore as A = B
    (A + B) (A - B) = A2 - AB
    (A + B) (A - B) = A ( A - B)
    Is simplified by (A - B)
    and there is obtained
    (A + B ) = A
    and as A = B
    A + A = A
    2 A = A

    A by simplifying found

        2 = 1

False , of course! To you to prove it ...


Answers : 

It is the simplification (AB) is illegal.
    What for ? because A = B then A - B = 0 .
    It has no right to simplify by 0 .
    Naughty course, but let's look at the following equation :
    2 x 0 0 x = 5
    If simplified by 0, we have 2 = 5
    or ... anything else since the product of any number by zero is zero !

The unmasked one is pink confusion !