Question 890782
Put all the expressions onto one side.


Note the critical  values of x at -1 and -2.


{{{4/(x+1)-3/(x+2)=0}}}, CHECK THE EQUALITY.  This may be another critical value.


Multiply both sides by LCD.
{{{4(x+2)-3(x+1)=0}}}
{{{4x+8-3x-3=0}}}
{{{x+5=0}}}
{{{x=-5}}}, possibly another critical point along with -1 and -2.


Look for truth or falseness in the intervals for {{{4/(x+1)<=3/(x+2)}}}.
x<=-5
{{{4/(-6+1)<3/(-6+2)}}}
{{{-4/5<-3/4}}}, TRUE.
{{{4/(-5+1)<3/(-5+2)}}}
{{{-1<-1}}, FALSE.  {{{x<-5}}}.

-5<=x<=-2
{{{4/(-3+1)<3/(-3+2)}}}
{{{-2<-3/2}}}, TRUE.
{{{4/(-2+1)<3/(-2+2)}}}, FALSE.  {{{x<>-2}}}.

-2<=x<=-1, {{{x<>-1}}}.


So far, you know {{{x<-5}}}  OR  {{{-5<x<-2}}}----- still not finished finding solutions for x.



CAN YOU FINISH THESE?

NEED ALSO TO CHECK

-2<=x<=-1, {{{x<>-1}}}.
-1<=x