*Instant 10 points* Just tell me how to solve this math problem.

The equation is
[ (x-2) / (x+2) ] >= 0
when I solve it I am getting x>=2, but my book shows two solutions, one is x>=2 and the other is x<-2, plz tell me how to get this 2nd solution.

Your solution probably looks something like
[(x-2)/(x+2)] >= 0
[(x-2)/(x+2)]*(x+2) >= 0*(x+2) = 0
(x-2) >= 0
x >= 2

But look at the second step--we multiplied by x+2. Is this positive or negative? If it's negative, we have to remember to switch the sign of the inequality. When is it negative? When x < -2. In that case, the rest becomes
(x-2) <= 0
x <= 2

Since we've already had to assume x < -2, that's the solution in this case.

p represents positive
n represents negative

p/p>=0
n/n>=0

Either (x-2) and (x+2) >=0 meaning (x-2)>=0 as clearly if this is true x+2 will also be because it is bigger. therefore x>=2
Or (x-2) and (x+2) <=0 meaning (x+2) <=0 as clearly this also meas x-2<=0 as it is smaller. therefore x<=-2

So x>=2 or x<=-2