Answer:
C
Step-by-step explanation:
Given
[tex]\frac{x}{x^2+3x+2}[/tex] + [tex]\frac{3}{x+1}[/tex] ← factor the denominator of first fraction
= [tex]\frac{x}{(x+1)(x+2)}[/tex] + [tex]\frac{3}{x+1}[/tex]
Multiply the numerator/ denominator of second fraction by (x + 2)
= [tex]\frac{x}{(x+1)(x+2)}[/tex] + [tex]\frac{3(x+2)}{(x+1)(x+2)}[/tex]
The denominators are now common, so add the numerators leaving the denominator, that is
= [tex]\frac{x+3x+6}{(x+1)(x+2)}[/tex]
= [tex]\frac{4x+6}{(x+1)(x+2)}[/tex] → with numerator 4x + 6 → C
