Final answer:
The numerator of the simplified sum of the terms x/(x²+3x+2) and 3/(x+1) is 4x + 6, which corresponds to choice C.
Step-by-step explanation:
To find the sum of the terms x/(x²+3x+2) and 3/(x+1), we need to determine a common denominator and then combine the terms. Observe that the denominator x²+3x+2 can be factored to (x+1)(x+2). Therefore, our second fraction, 3/(x+1), is missing the (x+2) to have a common denominator. The common denominator will be (x+1)(x+2).
Let's rewrite both fractions:
- The first term as x/(x+1)(x+2).
- The second term as 3(x+2)/(x+1)(x+2) to get the same denominator.
Now, add the numerators together:
x + 3(x+2)
Distribute the 3:
x + 3x + 6
Combine like terms:
4x + 6
The numerator of the simplified sum is therefore 4x + 6.