Final answer:
To factorize and simplify the rational expression, we can factorize the numerator and denominator separately. The simplified expression is (x+6)(x+2) / (x+3)(x²-3x+6).
Step-by-step explanation:
To factorize and simplify the rational expression (x²+8x+12)/(x³+3x-18), we need to first factorize the numerator and the denominator separately.
The numerator x²+8x+12 can be factored as (x+6)(x+2), and the denominator x³+3x-18 can be factored as (x+3)(x²-3x+6). So, the simplified expression is:
(x+6)(x+2) / (x+3)(x²-3x+6)