Find the lowest common denominator for each of the following expressions. Do not state
the restrictions or simplify. Show all your work.
2𝑥+1 / 𝑥^2−5𝑥−14 − 6𝑥 / 𝑥^2+3𝑥+2
To find the lowest common denominator of the given expressions, we need to factor the denominators and find the common factors.
The first denominator can be factored as:
x^2 - 5x - 14 = (x - 7)(x + 2)
The second denominator can be factored as:
x^2 + 3x + 2 = (x + 2)(x + 1)
To find the common factors, we take the intersections of the two sets of factors:
(x - 7), (x + 2), (x + 1)
Therefore, the lowest common denominator is:
(x - 7)(x + 2)(x + 1)