Question 62827
Please help me solve this problem: 
{{{(x+1)/(x-1)>=0}}}
Your intervals to test are found by finding what makes the fraction =0, by finding what makes the numerator=0.
x+1=0 
x+1-1=0-1
x=-1
and what makes the fraction undefined, what makes the denominator=0.
x-1=0
x-1+1=0+1
x=1  Keep in mind that x cannot=1
The possible intervals to our solution are:
(-infinity,-1], [-1,1), (1,infinity)
Test a point in the interval (-infinity,-1], like -2.
{{{(-2+1)/(-2-1)>=0}}}
{{{-1/-3>=0}}}
{{{1/3>=0}}}  This is true, so (-infinity,-1]  is part of the solutuion.
Test a point in the interval [-1,1), like 0.
{{{(0+1)/(0-1)>=0}}}
{{{1/-1>=0}}}
{{{-1>+0}}}  This is false, so the interval [-1,1) is NOT part of the solution.
Finally test a point in the interval (1,infinity), like 2.
{{{(2+1)/(2-1)>=0}}}
{{{3/1>=0}}}
{{{3>=0}}} is true, therefore the interval (1,infinity) is part of the solution.
Therefore the solution is:
(-infinity,-1]U(1,infinity)
Happy Calculating!!!