Question 731903
1+x divided by 1-x   greater than equal to to 1....

{{{(1+x)/(1-x)>=1}}}, you must permit the possiblities of 1-x being negative and 1-x being negative and check each of these conditions separately.  1-x must NOT be zero so x must NOT equal 1.  This value would be a critical point for x for checking a couple of intervals.


Letting 1-x>0, 1+x>=1*(1-x), and you can solve for x for this condition.
1+x>=1-x
1-1+x+x>=1-1-x+x
2x>=0
x>=0
Check this interval.  x=4, (1+4)/(1-4)=-5/3>=1 FALSE.

Letting 1-x<0, 1+x<=1*(1-x), and you can then solve for x in this condition.
1+x<=1-x
1-1+x+x<=1-1-x+x
2x<=0
x<=0
Check this interval.  x=-4, (1-4)/(1+4)=-3/5>=1 FALSE.


What about the interval, 0<=x<1?
Try x=(1/2).
(1+1/2)/(1-1/2)=(3/2)/(1/2)=3>=1? TRUE.


I must have made a mistake which I have not been able to find, but using the critical points of x at 0 and 1 and the three intervals around them seems to work well.  The solution is {{{ 0<=x<1}}}.