Помогите [tex]( \frac{x-1}{ x^{ \frac{1}{3} }-1 } + x^{ \frac{1}{3} } )* \frac{ x^{ \frac{1}{3} }-1 }{ x^{ \frac{2}{3} }-1 } [/tex]. Created by assema1998. algebra-ru

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assema1998 @assema1998

July 2022 1 8 Report

Помогите
[tex]( \frac{x-1}{ x^{ \frac{1}{3} }-1 } + x^{ \frac{1}{3} } )* \frac{ x^{ \frac{1}{3} }-1 }{ x^{ \frac{2}{3} }-1 } [/tex]

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nafanya2014

Verified answer

$x-1=(x ^{ \frac{1}{3} }) ^{3}-1=( x^{ \frac{1}{3} } -1)(x ^{ \frac{2}{3} }+ x^{ \frac{1}{3} } +1)$

$( \frac{x-1}{x ^{ \frac{1}{3} }-1 }+x ^{ \frac{1}{3} })= \frac{( x^{ \frac{1}{3} } -1)(x ^{ \frac{2}{3} }+ x^{ \frac{1}{3} } +1)}{x ^{ \frac{1}{3} }-1}+x ^{ \frac{1}{3} }=x ^{ \frac{2}{3} }+ x^{ \frac{1}{3} } +1+x ^{ \frac{1}{3} }= \\ \\ =x ^{ \frac{2}{3} }+ 2x^{ \frac{1}{3} } +1=(x^{ \frac{1}{3} } +1)^2$

$( \frac{x-1}{x ^{ \frac{1}{3} }-1 }+x ^{ \frac{1}{3} })\cdot \frac{x ^{ \frac{1}{3} }-1}{x ^{ \frac{2}{3} }-1}=(x ^{ \frac{1}{3} }+1) ^{2}\cdot \frac{x ^{ \frac{1}{3} }-1}{(x ^{ \frac{1}{3} }-1)(x ^{ \frac{1}{3} }+1)}=x ^{ \frac{1}{3} }+1$

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