
A.
3 
B.
4 
C.
2 
D.
3
Correct Answer: Option B
Explanation
(frac{x + 1}{3}) > (frac{1}{X + 3}) = (frac{x + 1}{3}) > (frac{x + 3}{X + 3})
= (x + 1)(x + 3)^{2} > 3(x + 3) = (x + 1)[x^{2} + 6x + 9] > 3(x + 3)
x^{3} + 7x^{2} + 15x + 9 > 3x + 9 = x^{3} + 7x^{2} + 12x > 0
= x(x + 3)9x + 4) > 0
Case 1 (+, +, +) = x > 0 , x + 3 > 0, x + 4 > 0
= x > 4 (solution only)
Case 2 (+, , ) = x > 0, x + 4
= x > 0, x
Case 3 (, +, ) = x 3, x
Case 4 (, , +) = x 0
= x 4 = x
combining the solutions 4