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.
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)
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)
Thanks
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