Final answer:
The factored form of the least common denominator needed to simplify the expression is (g + 5)(g - 3).
Step-by-step explanation:
The student asked to write the factored form of the least common denominator (LCD) needed to simplify the expression (g +1)/(g² + 2g -15) + (g + 3)/(g + 5). To find the LCD, we must first factor the denominators if possible.
For the first denominator g² + 2g - 15, we factor it as (g + 5)(g - 3). The second denominator is already a single term (g + 5).
Since both denominators have a (g + 5) term, the least common denominator will just be the product of the distinct factors. Therefore, the factored form of the least common denominator is:
(g + 5)(g - 3)
To simplify any expression with these denominators, we would ensure that each term has this LCD as its denominator before adding or subtracting any fractions.