Решите неравенство abs(x^2+x)<abs(x^2+3x+2)

$|x^2+3x+2|\ \textgreater \ |x^2+x|\Leftrightarrow (x^2+3x+2)^2\ \textgreater \ (x^2+x)^2\Leftrightarrow$

$(x+1)^2(x+2)^2-x^2(x+1)^2\ \textgreater \ 0\Leftrightarrow (x+1)^2((x+2)^2-x^2)\ \textgreater \ 0 \Leftrightarrow$

$(x+1)^2(x+2-x)(x+2+x)\ \textgreater \ 0\Leftrightarrow 2(x+1)^2(2x+2)\ \textgreater \ 0\Leftrightarrow$

$4(x+1)^3\ \textgreater \ 0\Leftrightarrow x+1\ \textgreater \ 0\Leftrightarrow x\ \textgreater \ -1$

Ответ: $(-1;+\infty)$