Question

Сократите дробь a^6-1 / a^4+a^2+1

Answer 1

$\dfrac{a^6-1}{a^4+a^2+1} = \dfrac{(a^3-1)(a^3+1)}{a^4+a^2+1} =\\ \\ \\ = \dfrac{(a-1)(a^2+a+1)(a+1)(a^2-a+1)}{a^4+a^2+1} = \dfrac{(a^2-1)(a^4+a^2+1)}{a^4+a^2+1} =\\ \\ \\ =a^2-1$