The LCD is x^2+3x+2 = (x+2)(x+1)
The goal is to get each fraction to have the denominator be equal to the LCD
Afterward we can add the fractions
x/(x^2+3x+2) + 3/(x+1)
x/((x+2)(x+1)) + 3/(x+1)
x/((x+2)(x+1)) + (3(x+2))/((x+2)(x+1))
(x+3(x+2))/((x+2)(x+1))
(x+3x+6)/(x^2+3x+2)
(4x+6)/(x^2+3x+2)
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Final Answer: 4x+6
Note: you can factor 4x+6 to get 2(2x+3)