We have a difference of fractions to combine and simplify. Just as we do when we have numerical expressions involving fractions to combine, we need to find the least common denominator (LCD) for the denominators given. We factor each denominator, and build our LCD from the factors found. Factoring the first denominator, we have t2 + 2t - 48 = (t - 6)(t + 8). Factoring the second denominator, we have 2t2 + 13t - 24 = (2t - 3)(t +). Thus, our LCD contains one factor each of (t - 6), (t + 8), and (2t - 3). Therefore, we have LCD = (t - 6)(t +)(2t - 3)