Question 976979
First, multiply left and right by  {{{(1/9)}}}.


{{{1/(h+1)>1}}}


Continuing,


{{{1/(h+1)-1>0}}}


{{{1/(h+1)-(h+1)/(h+1)>0}}}


{{{highlight_green(h/(h+1)>0)}}}
The critical values are the root which is 0, and the undefined value which is -1.  These form the intervals on h of  {{{h<-1}}}, {{{-1<h<0}}}, and {{{0<h}}}.  CHECK ANY ONE VALUE in each interval and determine if the value and the interval  will work in the ORIGINAL inequality.


Write again if any trouble doing that.