We need to solve the next given inequality:
[tex]\frac{x+8}{x-8}>0[/tex]
For rationals inequalities where one side is zero: We use the next property:
[tex]\frac{a}{b}>0[/tex]
Then
a>0 and b>0 or a<0 and b<0
Hence,
x+8> 0
Solve for x:
x>-8
and
x-8 >0
x>8
,
or
x+8<0
x<-8
and
x-8<0
x<8
Hence, the result is x>-8 or x>8.
The interval notation is (-∞,-8) U (8,∞).
