If #x=-5# then the denominator of the rational expression is zero and the quotient is undefined. So #-5# is not part of the solution set.
#color(white)()#
Case #bb(x < -5)#
If #x < -5# then #(x+5) < 0#
Multiply both sides of the inequality by #(x+5)# and reverse the inequality (since #(x+5) < 0#) to get:
#x+26 <= 0#
Subtract #26# from both sides to get:
#x <= -26#
So #(-oo, -26]# is part of the solution set.
#color(white)()#
Case #bb(x > -5)#
If #x > -5# then #(x+5) > 0#
Multiply both sides of the inequality by #(x+5)# to get:
#x+26 >= 0#
Subtract #26# from both sides to get:
#x >= -26#
Since #x > -5# this is already true.
So #(-5, oo)# is part of the solution set.
#color(white)()#
Conclusion
The solution set is:
#(-oo, -26] uu (-5, oo)#
