Question 152185
{{{ x/(x+1)>=3x }}}
then

{{{ x/(x+1)-3x>=0 }}}
then

{{{ (x-3x(x+1))/(x+1)>=0 }}}

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

sign of x*(-3x-2)is    --------0++++++0-----
.............................................-2/3...........0  
sign of x+1 is         --0+++++++++++++++
..........................-1

sign of f(x)          +++*-----0++++++0-----  (* symbol means does not exists)
.........................-1..........-2/3........0

then f is >=0 when x<-1 or -2/3<x<0