Question

find the lcd of this group of fractions

4/-9x and -3/7

Answer 1

To find the least common denominator (LCD) of the fractions \( \frac{4}{-9x} \) and \( \frac{-3}{7} \), we need to consider the denominators of both fractions: \(-9x\) and \(7\).

1. **Identify the denominators:**
- The first fraction has a denominator of \(-9x\).
- The second fraction has a denominator of \(7\).

2. **Factor the denominators:**
- \(-9x\) can be expressed as \(-1 \times 9 \times x\) or simply \(-9x\).
- \(7\) is already a prime number.

3. **Find the least common multiple (LCM):**
- The LCM of the absolute values of the denominators \(9x\) and \(7\) must be computed.
- The prime factorization of \(9\) is \(3^2\).
- Since \(7\) is prime, we take \(7\) as well.

4. **Combine the factors:**
- The LCM must include each factor at its highest power:
- From \(9\) (which is \(3^2\), we take \(3^2\)).
- From \(7\) (which is \(7^1\), we take \(7\)).

So, the LCM of \(9\) and \(7\) is:
\[
9 \times 7 = 63
\]

5. **Add the variable \(x\) from the first denominator:**
- Include \(x\) in the LCM since it is part of one of the denominators.

6. **Final LCD:**
- Therefore, the Least Common Denominator (LCD) is:
\[
-63x
\]

So, the least common denominator of the given fractions is \(-63x\).