(1) Before considering the inequality simplify the expression. Factor the numerator, and you get: x²+ 4x + 3/(-3-x) = (x+3)(x+1) / (- (x+3) ) which is "undefined" (equal to 0/0) when x = - 3. It's defined for all other values of x, and it simplifies to -(x+1).
(2) Now apply the inequality to the simplified expression to get -(x+1) > 0. Rewrite (multiply both sides of the inequality by -1) as x+1 < 0. Solve that to get x< - 1.
Combine (1) and (2) to get x < -1 and x is undefined for x= -3. There are no other answers.
You can also solve problems like this by "substitutions" with the goal of eliminating options. Try for x a negative number less than -3, and note that it satisfies the inequality so this eliminates D. Note that in the post above the choice x = -2 is used to eliminate D. However the computation is incorrect for x = -2. It is a valid solution, as are all values less than -1. But D says the numbers MUST be in the range -1 to -3.