Linear algebra students everywhere are triggered by this classic mathematical troll move. The equation shows y = (y·u₁/u₁·u₁)u₁ + (y·u₂/u₂·u₂)u₂ where those fractions are screaming to be simplified. But textbook authors refuse to cancel the u's because they're not actually the same term - one is a dot product in the numerator and another is in the denominator.
It's like thinking you can cancel the 2's in 2+3/2+5. You can't! Math professors secretly giggle every time a student makes this mistake and then has to sheepishly erase their work. The projection formula may look tempting, but those u's are staying right where they are!
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