There are 2 critical points x= 3 and x= -2,

and there are 3 intervals  (,),  (-2,3)  and  (,).


We consider all three intervals one after another, moving from the left to the right.


1.  In the interval  (,)  the numerator  (x-3) is negative; the denominator  (x+2) is negative, too.

    Hence, the ratio    is positive.



2.  In the interval  (-2,3)  the numerator  (x-3) is negative; the denominator  (x+2) is positive.

    Hence, the ratio    is negative.



3.  In the interval  (,)  the numerator  (x-3) is positive; the denominator  (x+2) is positive, too.

    Hence, the ratio    is positive.



4.  Thus your answer is:  The solution of the given inequality is this intervals union  (,)  U (,).