Question 1020598
Make it into relation to zero.


{{{1/(x+2)>x+2}}}
{{{1/(x+2)-x-2>0}}}
{{{1/(x+2)-x(x+2)/(x+2)-2(x+2)/(x+2)>0}}}


{{{(1-x(x+2)-2(x+2))/(x+2)>0}}}


{{{(1-x^2-2x-2x-4)/(x+2)>0}}}


{{{1-x^2-4x-4)/(x+2)>0}}}


{{{(-x^2-4x-3)/(x+2)>0}}}


{{{(-1)(x^2+4x+3)/(x+2)>0}}}


Multiply left and right members by {{{-1}}} and REVERSE the direction of the inequality symbol...


{{{highlight_green((x^2+4x+3)/(x+2)<0)}}}-------this is the form which you analyze.


Continue with factorization.
{{{((x+1)(x+3))/(x+2)<0}}}
The critical values of x are  -1, -2, -3.