Question

Which answer includes the intervals that contain the solution to the inequality?

Answer 1

The correct option is D (-∞,-3)∪(-1,1)

Explanation:

Given,

`(x^(2)-1 )/(3x+9)` ≤ 0

To find the solution.

The solution could be found if

`x^(2) -1` ≤ 0 and

3x+9 ≠ 0 [if the denominator is 0, it gives ∞ as solution]

Now,

`x^(2) -1` ≤ 0

or, (x+1)(x-1) ≤0

or, x ≤1 and x≤-1

Both of the above condition holds is x≤1

Again,

3x+9≠0

or, x≠-3

All the conditions gold for the values (-∞,-3)∪(-1,1)

Hence the correct option is D.