Final answer:
To simplify the given expression, factor the numerator and denominator and then cancel out the common factors to get (x+3) / (x+2).
Step-by-step explanation:
To simplify the given expression, we will first simplify each term individually. We can start by factoring the numerator and denominator:
x² - 9 = (x-3)(x+3)
3x² + 8x - 3 = (3x - 1)(x + 3)
Next, we can rewrite the division as multiplication by the reciprocal:
(x-3)(x+3) / (x-3)(x+2)
Now we can cancel out the common factors:
= (x+3) / (x+2)
Therefore, the simplified expression is (x+3) / (x+2).