Сократить дробь: x^2-x+1 / x^4+x^2+1. Created by abduqodirovaziz. algebra-ru

x^4+x^2+1...

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August 2021 1 25 Report

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x^2-x+1 / x^4+x^2+1

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dtnth

Verified answer

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

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