Question

(n^4-9n3+12n^2+9n-13):(n^4-10n^3+22n^2-13n)

Answer 1

Числитель:
n^4 - 9n^3 + 12n^2 + 9n - 13 = n^4 - n^3 - 8n^3 + 8n^2 + 4n^2 - 4n + 13n - 13 =
= (n - 1)(n^3 - 8n^2 + 4n + 13) = (n - 1)(n^3 + n^2 - 9n^2 - 9n + 13n + 13) =
= (n - 1)(n + 1)(n^2 - 9n + 13)
Знаменатель:
n^4 - 10n^3 + 22n^2 - 13n = n(n^3 - n^2 - 9n^2 + 9n + 13n - 13) =
= n(n - 1)(n^2 - 9n + 13)
Получаем
$frac{(n-1)(n+1)(n^2-9n+13)}{n(n-1)(n^2-9n+13)} = frac{n+1}{n}$