Final answer:
To factorize and simplify the rational expression ˣ³+8x+12)/ˣ³+3x-18), factor the numerator and the denominator separately, cancel out the common factors, and simplify.
Step-by-step explanation:
To factorize and simplify the rational expression ˣ³+8x+12)/ˣ³+3x-18), we first factor the numerator and the denominator separately. The numerator can be factored as (x+2)(x²-2x+6) and the denominator can be factored as (x+6)(x-3). Then, we can simplify the expression by canceling out the common factors in the numerator and denominator. The simplified expression is (x+2)/(x-3).