Answer:
The possible test points are -5,-3.5 , -2.5,0,5
Step-by-step explanation:
Given : The inequality [tex]\frac{x^2-9}{x^2+6x+8}>0[/tex] can be factored as
(x + 3)(x - 3) (x + 4)(x + 2) > 0
To find : Which are possible test points?
Solution : The inequality factored as
[tex]\frac{x^2-9}{x^2+6x+8}>0[/tex]
[tex]\frac{(x + 3)(x - 3)}{(x + 4)(x + 2)}>0[/tex]
The critical points are defined as when we equation the factor to zero then the value of x is the critical point.
So, x+3=0 ⇒ x=-3
x-3=0 ⇒ x=3
x+4=0 ⇒ x=-4
x+2=0 ⇒ x=-2
The critical points of the given inequality are -4,-3,-2,3
The possible test points are the points except critical points.
Therefore, Out of the given options
The possible test points are -5,-3.5 , -2.5,0,5 as they are not critical points.
