To find the least common denominator (LCD) of the fractions 5/2(x-2), 7/2x, and 3/4, we need to factor and find the least common multiple of the denominators of each fraction.
The denominators are 2(x-2), 2x, and 4. We can simplify 2(x-2) to 2x-4.
Now, the factors of the denominators are:
- 2x-4 = 2 * (x-2)
- 2x = 2 * x
- 4
The least common multiple of 2 * (x-2), 2 * x, and 4 is 4 * 2 * (x-2) = 8(x-2).
Therefore, the LCD of the fractions 5/2(x-2), 7/2x, and 3/4 is 8(x-2).
find the lcd
5/2(x-2) and 7/2x and 3/4
3 answers
remember, the LCD has to have all the factors of the denominators but with no extras. And treat x-2 as a single quantity.
Apologies for the oversight. Let's factor and find the least common denominator (LCD) correctly.
The denominators are 2(x-2), 2x, and 4. Factoring out the denominators:
- 2(x-2) = 2x-4
- 2x
- 4
To find the LCD, we need to consider all the factors but with no extras. We notice that the factors of 2(x-2) are 2, x-2, and could also have a factor of x to match the other denominators’ x terms. Therefore, we'll include the necessary x factor.
The final LCD is the least common multiple of 2 * x * (x-2) which equals 2x(x-2).
Therefore, the LCD of the fractions 5/2(x-2), 7/2x, and 3/4 is 2x(x-2).
The denominators are 2(x-2), 2x, and 4. Factoring out the denominators:
- 2(x-2) = 2x-4
- 2x
- 4
To find the LCD, we need to consider all the factors but with no extras. We notice that the factors of 2(x-2) are 2, x-2, and could also have a factor of x to match the other denominators’ x terms. Therefore, we'll include the necessary x factor.
The final LCD is the least common multiple of 2 * x * (x-2) which equals 2x(x-2).
Therefore, the LCD of the fractions 5/2(x-2), 7/2x, and 3/4 is 2x(x-2).