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They are not. Factoring the expressions allows the extraction of potential similar components in the numerator and denominator, meaning that they can be simplified. I understand what I am talking about because this is the last thing I learned in my algebra 2 class before break.
What does QED mean?
well im taking pre-calculus, so there is something i have learned that you may not have: even if the numerator and the denominator share a factor, they sort of cancel out, but not really, as seen above, with (x-1)²/(x-1) being different
quod erat demonstrandum, meaning "that which was to be demonstrated", i.e. “im done proving the thing i was trying to”
all good