Помогите пожалуйста решить неравенство1-1/(x+2)>=1/((1+1/(x+1))(x-1)). Created by olyalavyagina. algebra-ru

(x+1))(x-1))...

olyalavyagina @olyalavyagina

July 2022 1 10 Report

Помогите пожалуйста решить неравенство
1-1/(x+2)>=1/((1+1/(x+1))(x-1))

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Матов

Verified answer

$1-\frac{1}{x+2} \geq \frac{1}{(1+\frac{1}{x+1})(x-1)}\\
 \frac{x+2-1}{x+2} \geq \frac{1}{x-1+\frac{x-1}{x+1}}\\
 \frac{x+1}{x+2} \geq \frac{1}{\frac{x^2+x-2}{x+1}}\\
\frac{x+1}{x+2} \geq \frac{x+1}{(x+2)(x-1)}\\\\
x \neq -2\\
x \neq 1\\
(x+1)(x-1) \geq x+1\\
x^2-1 \geq x+1\\
 x^2-x-2 \geq 0\\
 (x-2)(x+1) \geq 0\\
 
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методом интервалов , получаем
$(-oo;2)\ U \ (-1;1) \ U \ [2;+oo)$

1 votes Thanks 1

olyalavyagina А -1 тоже включительно?

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