Is 2 = 1?

Algebra Level 1

What is wrong with the following "proof"?

Let $a = b=1$ , then $a+b=b.$

Step 1: $a^2 = ab$
Step 2: $a^2 - b^2 = ab - b^2$
Step 3: $(a+b)(a-b) = b(a-b)$
Step 4: $a+b= \dfrac{b(a-b)}{a-b}$
Step 5: $a+b = b$

Conclusion: By substituting in $a = b = 1,$ we have $1+1 = 1 \implies 2 = 1.$