Why is This Proof Wrong?

In "proofs" of this sort, there are several common things that go astray, among them:
1) Inadvertent division by zero, as when "canceling" factors from both sides of an equation.
2) Introduction of extraneous solutions, as in squaring both sides of an equation, which admits both positive and negative square roots, one of which may not satisfy the original equation. (There are videos about extraneous solutions.)
3) Using unmotivated steps such as -1/1=1/-1; a sure clue some sleight-of-hand is about to occur.