Question

How can I find the least common denominator of (x+1)/(3x-1), (x)/(x-1), and (4)/(3)?

Answer 1

Here the 3 denominators have no common factors. Therefore, the least common denominator is just the product of the three denominators.

Answer 2

Thank you, for some reason since the beginning of the chapter we started, I have had troubles finding the LCD, I understand what I'm trying to get but sometimes actually finding what I'm trying to get causes issues, if that makes any sense.

Answer 3

Example:
Find LCD of 1/2, 1/3, 1/5
The denominators are 2, 3 and 5. They have no factors in common.
LCD = 2 * 3 * 5 = 30

Find LCD of 1/2, 1/4, 1/5
2: 2
4: 2 * 2 (factor includes the factor of previous term. So the previous 2 can be dropped)
5 : 5
So LCD = 2 * 2 * 5 = 20

Find LCD of 1/x, 1/7, 1/(x-3)
Denominators are: x, 7 and (x-3).
No common factors. So LCD = x * 7 * (x-3) = 7x(x-3)

Find LCD of 1/x, 1/(7x^3), 1/{x^2(x-3)}
x: x
7x^3: 7 * x * x * x (contains factors of previous term. Ignore previous term).
x^2(x-3): x * x * (x-3) (x * x is contained in previous term. Ignore that part)

LCD =7 * x * x * x * (x-3) = 7x^3(x-3)