Final answer:
To simplify the given rational expression, factor the numerator and denominator and cancel out common factors. The simplified expression is 3/(4x+1).
Step-by-step explanation:
To simplify the given rational expression 3x+9/4x^2+13x+3, you need to factor the numerator and denominator and then cancel out any common factors.
1. Factor the numerator and denominator if possible.
2. Cancel out common factors.
3. Simplify any remaining terms if possible.
4. Check the answer to see if it is reasonable.
In this case, we can factor the numerator as 3(x+3) and the denominator as (x+3)(4x+1). The common factor x+3 can be canceled out, leaving us with the simplified expression 3/(4x+1).