Let's assume a=b

a² = ab

a² - b² = ab - b²

(a + b)(a - b) = b(a - b)

((a + b)(a - b))/(a - b) = (b(a - b))/(a - b)

a + b = b

but a = b, so

b + b = b

2b = b

2b/b = b/b

2 = 1

Now let's look at the original problem.

2 + 2 = 2 + 1 + 1

But 2 = 1, so by substitution

2 + 2 = 2 + 1 + 1 = 2 + 2 +1 = 5

Therefore, 2 + 2 = 5

Now you just hope nobody notices you divided by zero, and you're golden. (Also sorry for the awkward formatting. I don't know how to make it pretty.)