Упростить выражение (a+1/a^4+a^3+a^2) / (1/a^5-a^2. Created by vallenkog. algebra-ru

a^5-a^2...

vallenkog @vallenkog

August 2022 2 6 Report

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(a+1/a^4+a^3+a^2) / (1/a^5-a^2

matilda17562

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Решение:

$\frac{a + 1}{a^{4} + a^{3} + a^{2}} : \frac{1}{a^{5} - a^{2}} = \frac{a + 1}{a^{2}(a^{2} + a + 1)} : \frac{1}{a^{2}(a^{3} - 1)} = \frac{(a + 1) *a^{2}(a^{3} - 1) }{a^{2}(a^{2} + a + 1)} = \frac{(a + 1) *(a - 1)*(a^{2} + a + 1) }{(a^{2} + a + 1)} = (a + 1) *(a - 1) = a^{2} - 1.$

Ответ: $a^{2} - 1.$

3 votes Thanks 2

skvrttt

$\mathtt{\frac{(a+1)(a^5-a^2)}{a^4+a^3+a^2}=\frac{a^2(a+1)(a^3-1)}{a^2(a^2+a+1)}=\frac{(a+1)(a-1)(a^2+a+1)}{(a^2+a+1)}=a^2-1}$

0 votes Thanks 0

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