Question

Hello, I need some assistance with this homework question please for precalculusHW Q12

Answer 1

We need to solve the next given inequality:

`(x+8)/(x-8)>0`

For rationals inequalities where one side is zero: We use the next property:

`(a)/(b)>0`

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,∞).