1. Let a and b be equal non-zero quantities
a = b
2. Multiply through by a
a^2 = ab
3. Subtract b^2
a^2 - b^2 = ab - b^2
4. Factor both sides
(a - b)(a + b) = b(a - b)
5. Divide out (a - b)
a + b = b
6. Observing that a = b
b + b = b
7. Combine like terms on the left
2b = b
8. Divide by the non-zero b
2 = 1

Question

1. Let a and b be equal non-zero quantities
a = b 
2. Multiply through by a
a^2 = ab 
3. Subtract b^2 
a^2 - b^2 = ab - b^2 
4. Factor both sides
(a - b)(a + b) = b(a - b) 
5. Divide out (a - b) 
a + b = b 
6. Observing that a = b 
b + b = b 
7. Combine like terms on the left
2b = b 
8. Divide by the non-zero b
2 = 1

anonymous · Answer

"a = b"$$
a-b=0
$$
"5. Divide out (a - b)"
Divide out $0$

No

anonymous · Answer

got it!ty

anonymous · Answer

$$
(a - b)(a + b) = b(a - b)  \implies \frac{a - b}{a-b}(a + b) = b 
$$
You say $0/0=1$, but I say: $0/0=1/2$

anonymous · Answer

$$
\frac 12(a+b)=b\
\frac 12(b+b)=b\
b=b
$$And I'm right.

anonymous · Answer

$$
0/0
$$Is an indeterminate form.  In this case we can determine that is is $1/2$.

anonymous · Answer

ty