Найдите значение выражения:[tex] \frac{a ^{3} - 1}{a ^{3} - 2a^{2} + a } \div (( {a - 1)}^{0} + {(a - 1)}^{ - 1} )[/tex]при а = - 3. Created by 1vikusenok1. algebra-ru

tex]при а =

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Найдите значение выражения:
[tex] \frac{a ^{3} - 1}{a ^{3} - 2a^{2} + a } \div (( {a - 1)}^{0} + {(a - 1)}^{ - 1} )[/tex]
при а = - 3

Answers & Comments

solving05

Ответ:

Объяснение:

$\frac{a^3-1}{a^3-2a^2+a}/((a-1)^0+(a-1)^{-1})=\frac{(a-1)(a^2+a+1)}{a(a^2-2a+1)}/(1+\frac{1}{a-1})=\\=\frac{(a-1)(a^2+a+1)}{a(a-1)^2}/(1+\frac{1}{a-1})=\frac{a^2+a+1}{a(a-1)}/(\frac{a-1+1}{a-1})=\\=\frac{a^2+a+1}{a(a-1)}*(\frac{a-1}{a})=\frac{a^2+a+1}{a^2}=1+\frac{1}{a}+\frac{1}{a^2}.\\a=-3;1-\frac{1}{3}+\frac{1}{9}=\frac{9-3+1}{9}=\frac{7}{9}$

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