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  • Truscape@lemm.eeOPto196@lemmy.blahaj.zoneMathematical Rule
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    29 days ago

    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.