From a corkboard at my college campus.
It’s been like 20 years since I’ve done math like this. Can someone smarter than me remind me why this is wrong?
Cancelation between a numerator and denominator can only occur when both terms are multiplied as a whole, not simply added.
In this case, the polynomial at the top needs to be converted to the root multiplication that lead to it: (x+1)^2, and the denominator needs to complete the square: (x-1)(x+1)+4, which would still be unable to have terms canceled (as there is still addition in the denominator that cannot be removed), so the original form is the valid answer.
It’s a common thing drilled into students during these courses that you cannot simply cancel out terms at will - you have to modify polynomials first.
I did not understand a single word of that but thank you
Numerator - top half of a fraction
Denominator - bottom half of a fraction
Roots of a polynomial - multiplying two terms of (x+some constant)(x+some constant) should equal the equation with a primary term of x^2
“Completing the square” - Attempting to find roots of a difficult polynomial (in the case of that equation, finding 2 easy roots and adding a constant at the end of the denominator)
Also Jia tan lol, XZ utils backdoor username?
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Thanks
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Shhhhhh I’m on the run. The feds won’t look on blahaj.zone because they’re afraid of DEI accusations.
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You can cancel out multipliers that way, but not additions.
In addition to the other great answers, you can really drive the intuition about how wrong this is in students/kids with simple examples:
x+2/x+1– cancel thexincorrectly and this always equals 2, which should fail the smell check immediately, verify with a couple values ofx.x+1/xcancel thexincorrectly andundefined.Been a while for me too. But the division is probably what breaks it. If X = 3, you get 17/12 vs 7/3.
Around age 12 I read in a recreational maths book that 16/64=16̸/6̸4=1/4 works and I was lucky to encounter this at school while solving a problem on a whiteboard. This is not the case for this fraction but I wonder if there are any non-trivial examples of polynomial division where this works.
Man. I miss when this was the most difficult math thing. Fuck triple integrals.
I fucking hate polynomials.
