Final answer:
To find the least common denominator of the fractions x+2 / (x²+2x-3) and (x-4)/(x²+5x+6), we factor both denominators to find (x+3)(x-1) and (x+2)(x+3) respectively. The LCD includes (x-1), (x+2), and (x+3) as the distinct linear factors.
Step-by-step explanation:
To find the least common denominator (LCD) of the fractions x+2 / (x²+2x-3) and (x-4)/(x²+5x+6), we first need to factor the denominators if possible. Notice that both denominators are quadratic expressions that can potentially be factored into binomials.
The first denominator x²+2x-3 factors into (x+3)(x-1), and the second denominator x²+5x+6 factors into (x+2)(x+3).
Therefore, the LCD must include each distinct linear factor the greatest number of times it occurs in any single factorization. That is, we include each of (x-1), (x+2), and (x+3) exactly once, because none of the factors are repeated in either denominator. So, the LCD of the two given fractions is (x-1)(x+2)(x+3).