Сократите дробь: [tex] \frac{x^4-y^4}{x^3+xy^2-x^2y-y^3} [/tex]. Created by Катя1200. algebra-ru

tex]...

Катя1200 @Катя1200

July 2022 1 6 Report

Сократите дробь:
[tex] \frac{x^4-y^4}{x^3+xy^2-x^2y-y^3} [/tex]

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mukus13

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$\frac{x^4-y^4}{x^3+xy^2-x^2y-y^3}= \frac{(x^2-y^2)(x^2+y^2)}{(x^3-x^2y)+(xy^2-y^3)}= \frac{(x^2-y^2)(x^2+y^2)}{x^2(x-y)+y^2(x-y)}=$
$=\frac{(x^2-y^2)(x^2+y^2)}{(x-y)(x^2+y^2)}= \frac{x^2-y^2}{x-y} = \frac{(x-y)(x+y)}{x-y} =x+y$

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