In order for  g(x)  be positive,  both the numerator and denominator should be EITHER both positive, OR both negative.


So, we consider two cases.


Case (a).  x+8 > 0  AND  x+2 > 0.

     The solution set to these two inequalities is  {x > - 8}  AND  {x > - 2}.

     The last two inequalities are EQUIVALENT to  one single inequality  x > -2.



Case (b).  x+8 < 0  AND  x+2 < 0.

     The solution set to these two inequalities is  {x < - 8}  AND  {x < - 2}.

     The last two inequalities are EQUIVALENT to  one single inequality  x < -8.



Thus the final solution to your problem is this:


    {x < -8}  or  {x > -2},


Or in the interval form


    (-oo,-8) U {-2,oo)    (union of two sets).