Find the sum of the terms. x/x^2+3x+2 + 3/x+1
the numerator of the simplified sum
a) x + 3
b) 3x + 6
c) 4x + 6
d) 4x + 2.

We are asked to determine the numerator of the simplified sum and the answer is the letter "C" which is "4X + 6". To get the answer, the solution is shown below:
We have given equation as:
 x / (x²+3x + 2) + 3/(x+1) , we need to factor out the denominator of the first term such as x²+3x+2 = (x+2) (x+1)
x / (x+3)(x+1)  + 3/(x+1) 
Perform combining of terms such as:
    x + 3(x+2)          x + 3x +6           4X + 6
= =
    (x+2) (x+1)      (x+2)(x+1)          (x+2)(x+1)

Therefore, the numerator simplified sum is "4X + 6".