Question
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
5 / 𝑥−2 + 3 / 𝑥^2−4
Answers
GPT 3.5
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).
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).