Question

what is the numerator of the simplified sum?\\(\frac{x}{x^2 + 3x + 2} + \frac{3}{x + 1}\\)\\(\bigcirc\\ x + 3\\)\\(\bigcirc\\ 3x + 6\\)\\(\bigcirc\\ 4x + 6\\)\\(\bigcirc\\ 4x + 2\\)

Explanation:

Step1: Factor the quadratic denominator

Factor $x^2+3x+2$ into $(x+1)(x+2)$

Step2: Find common denominator

Rewrite $\frac{3}{x+1}$ with denominator $(x+1)(x+2)$:
$\frac{3(x+2)}{(x+1)(x+2)}$

Step3: Combine the fractions

Add the numerators over the common denominator:
$\frac{x + 3(x+2)}{(x+1)(x+2)}$

Step4: Simplify the numerator

Expand and combine like terms:
$x + 3x + 6 = 4x + 6$

Answer:

4x+6