Решение неравенства имеет вид

$\frac{3}{1+|x+3|} \ \textless \ 1 \\ 3\ \textless \ 1+|x+3| \\ 3 - 1 \ \textless \ |x+3| \\ 2\ \textless \ |x+3| \\ |x+3| \ \textgreater \ 2 \\ \left[\begin{array}{ccc}x+3 \ \textgreater \ 2 \\x+3\ \textless \ -2 \end{array}\right \\ \left[\begin{array}{ccc}x \ \textgreater \ -1 \\x\ \textless \ -5 \end{array}\right \\$

x∈ ( - ∞ ; -5 ) ∪ ( -1 ; + ∞ )