Find the lowest common denominator for each of the following expressions. Do not state
the restrictions or simplify. Show all your work.
𝑥+3 / x^2−9 + 𝑥^2−6𝑥+8 / 𝑥^2−3𝑥−4
To find the lowest common denominator for the given expressions, we need to find the least common multiple (LCM) of the denominators.
First, let's factor each denominator:
x^2 - 9 = (x + 3)(x - 3)
x^2 - 3x - 4 = (x - 4)(x + 1)
The LCM of (x + 3)(x - 3) and (x - 4)(x + 1) is their product, since they have no common factors.
LCM = (x + 3)(x - 3)(x - 4)(x + 1)