Разложить: a^2+b^2/a^2-b^2-a-b/a+b =. Created by milana2014. algebra-ru

a+b =...

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July 2022 1 19 Report

Разложить: a^2+b^2/a^2-b^2-a-b/a+b =

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$\frac{a^2+b^2}{a^2-b^2}-\frac{a-b}{a+b}=\frac{a^2+b^2}{(a-b)(a+b)}-\frac{a-b}{a+b}=\frac{a^2+b^2-(a-b)^2}{(a-b)(a+b)}=\frac{a^2+b^2-a^2+2ab-b^2}{(a-b)(a+b)}=\\\ =\frac{2ab}{(a-b)(a+b)}=\frac{2ab}{a^2-b^2}$

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