Find the lowest common denominator for each of the following expressions. Do not state the restrictions or simplify. Show all your work.
5 / 𝑥−2 + 3 / 𝑥^2−4
To find the lowest common denominator (LCD) for the two expressions, we need to determine the least common multiple (LCM) of the denominators.
The first denominator is (𝑥 − 2), and the second denominator is (𝑥^2 − 4).
To find the LCM in this case, we need to factor the second denominator:
𝑥^2 − 4 = (𝑥 − 2)(𝑥 + 2)
So, the LCM of the denominators is (𝑥 − 2)(𝑥 + 2).
The LCD for the two expressions is (𝑥 − 2)(𝑥 + 2).