Answer:
(x + 3)(x - 1)(x + 2)
Step-by-step explanation:
The fractions are:
[tex]\dfrac{x + 2}{x^{2} + 2x - 3} \text{ and } \dfrac{x - 7}{x^{2} + 5x + 6}[/tex]
Factor each denominator
[tex]x^{2} + 2x - 3 = (x + 3)(x - 1)\\x^{2} + 5x + 6 = (x + 3)(x + 2)[/tex]
We must find the least common multiple of the denominators. We take the maximum power of each separate factor.
Factors of first fraction = (x + 3) × (x - 1)
Factors of second fraction = (x + 3) × (x + 2)
LCM = (x + 3)(x - 1)(x + 2)
The lowest common denominator of the two fractions is (x + 3)(x - 1) (x + 2).
