Докажите тождество: (4a/a^a-1+a-1/a+1)*2a/a+1-a/a-1-a/a^2-1=a^2/a^2-1. Created by daschenka26. algebra-ru

a^2-1...

daschenka26 @daschenka26

August 2022 1 1 Report

Докажите тождество:
(4a/a^a-1+a-1/a+1)*2a/a+1-a/a-1-a/a^2-1=a^2/a^2-1

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kmike21

Verified answer

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

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