Question

Решите неравенство, пожалуйста
$\frac{1 - x}{ {(x +1)}^{2} } < 1$

Answer 1

$\frac{1-x}{(x+1)^2} \ \textless \ 1 \\ \\ 1- \frac{1-x}{(x+1)^2}\ \textgreater \ 0 \\ \\ \frac{(x+1)^2-1+x}{(x+1)^2} \ \textgreater \ 0 \\ \\ \frac{x^2+2x+1-1+x}{(x+1)^2}\ \textgreater \ 0 \\ \\ \frac{x^2+3x}{(x+1)^2}\ \textgreater \ 0 \\ \\ \frac{x(x+3)}{(x+1)^2}\ \textgreater \ 0 \\ \\ ++++(-3)---(-1)---(0)++++ \\ \\ x\in(-oo;-3)U(0;+oo)$