Question

find the lcd of this group of fractions.

5/4(x-3) and 1/4 and 7/x-3

Answer 1

To find the least common denominator (LCD) of the fractions \( \frac{5}{4(x-3)} \), \( \frac{1}{4} \), and \( \frac{7}{x-3} \), we need to identify the denominators of each fraction:

1. The denominator of the first fraction is \( 4(x-3) \).
2. The denominator of the second fraction is \( 4 \).
3. The denominator of the third fraction is \( x-3 \).

Next, we will find the least common denominator by taking all unique factors from each denominator:

- From \( 4(x-3) \), we have the factors \( 4 \) and \( (x-3) \).
- From \( 4 \), we have the factor \( 4 \) (which we already have).
- From \( x-3 \), we have the factor \( (x-3) \) (which we already have).

Combining the unique factors, we find that the least common denominator is:

\[
LCD = 4(x-3)
\]

Thus, the least common denominator of the fractions \( \frac{5}{4(x-3)} \), \( \frac{1}{4} \), and \( \frac{7}{x-3} \) is \( \mathbf{4(x-3)} \).