The correct option is D (-∞,-3)∪(-1,1)
Step-by-step explanation:
Given,
[tex]\frac{x^{2}-1 }{3x+9}[/tex] ≤ 0
To find the solution.
The solution could be found if
[tex]x^{2} -1[/tex] ≤ 0 and
3x+9 ≠ 0 [if the denominator is 0, it gives ∞ as solution]
Now,
[tex]x^{2} -1[/tex] ≤ 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.
