Question

Сократить дробь:
x^2-x+1 / x^4+x^2+1

Answer 1

$x^4+x^2+1=x^4+x^2+1+x^2-x^2=\\(x^4+2x^2+1)-x^2=\\((x^2)^2+2*x^2*1+1^2)-x^2=\\(x^2+1)^2-x^2=\\((x^2+1)-x)((x^2+1)+x)=\\(x^2-x+1)(x^2+x+1)$
тому
$frac{x^2-x+1}{x^4+x^2+1}=\\frac{x^2-x+1}{(x^2-x+1)(x^2+x+1)}=\\frac{1}{x^2+x+1}$