Question

Find the least common denominator of the rational expressions​ below:
StartFraction 20 Over 3 x plus 15 EndFraction
and StartFraction negative 18 Over 5 x plus 25 EndFraction

Answer 1

To find the least common denominator (LCD) of the rational expressions

\[
\frac{20}{3x + 15} \quad \text{and} \quad \frac{-18}{5x + 25},
\]

we first need to factor the denominators.

### Step 1: Factor the denominators

1. **For \(3x + 15\)**:
\[
3x + 15 = 3(x + 5).
\]

2. **For \(5x + 25\)**:
\[
5x + 25 = 5(x + 5).
\]

### Step 2: Identify the denominators

Now we have the denominators:
- \(3(x + 5)\)
- \(5(x + 5)\)

### Step 3: Determine the LCD

The least common denominator will be the product of the highest powers of all factors in the denominators.

- The factor \(3\) appears in the first denominator.
- The factor \(5\) appears in the second denominator.
- The factor \(x + 5\) is common to both denominators.

Therefore, the LCD is given by:
\[
\text{LCD} = 3 \times 5 \times (x + 5) = 15(x + 5).
\]

### Final Answer

The least common denominator of the rational expressions is:

\[
\boxed{15(x + 5)}.
\]