Question

Сократить дробь (a^3-1)/(a^4-a^2-2*a-1)

Answer 1

Разложим:
a^4 -a² -2a -1 =a^4 -(a² +2a +1) =a^4 -(a +1)² =

=(a² -(a+1))×(a² +(a+1)) =

=(a² -a -1)(a² +a +1)

a^3 -1 =(a -1)(a² +a +1)

решение:

(a-1)(a²+a+1) /(a²-a-1)(a²+a+1) =

=(a -1) /(a² -a -1)

Answer 2

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

$=\frac{(a-1)(a^2+a+1)}{[(a^2)-(a+1)]*[(a^2)+(a+1)]} =\frac{(a-1)*(a^2+a+1)}{(a^2-a-1)*(a^2+a+1)} =$

$=\frac{a-1}{a^2-a-1}$