.
>= 
has the domain x =/= -2 and x =/= 2 and is equivalent to (moving the right part to the left)
- >= 0
Write with the common denominator
>= 0.
Simplify step by step
>= 0,
>= 0,
>= 0. (1)
Simplifying is completed. Next we start analyzing.
The critical points, where the rational function (1) changes its sign, are the points -2, 0, 2 and 4.
They divide the number line in 5 intervals.
1) Interval (
,
).
All four separate factors are negative, hence, the function is POSITIVE.
Thus this interval IS the part of the solution.
2) Interval (,
).
One factor, (x+2) is positive; the other 3 factors are negative; hence, the function is NEGATIVE.
Thus this interval is NOT the part of the solution.
3) Interval [,
).
Two factors, (x+2) and x, are positive; the other 2 factors are negative; hence, the function is POSITIVE.
Thus this interval IS the part of the solution.
Moving forward along the number line interval after interval, and analyzing by the similar way, you get the
ANSWER. The solution is the union of the following intervals:
(,) U [,) U [
,
).
Completed, explained and solved.
/\/\/\/\/\/\/\/
Do you understand now why the forum requires one and only one problem per post ?
Because otherwise you will get a mess.
