Final answer:
To simplify the given expression, the least common denominator is found by factoring the quadratic expression and determining the overlapping factors. The least common denominator is the product of these factors, which in this case is (g + 5)(g - 3).
Step-by-step explanation:
The question asks to find the factored form of the least common denominator (LCD) needed to simplify the expression (g + 1)/(g^2 + 2g - 15) + (g + 3)/(g + 5). To do this, we need to factor the quadratic in one of the denominators and determine the LCD that both denominators can divide into. The quadratic g^2 + 2g - 15 factors into (g + 5)(g - 3). So, the LCD for the two denominators, (g + 5)(g - 3) and (g + 5), is (g + 5)(g - 3) because it incorporates both factors. This means we can use the LCD to combine the two fractions into one.