Ask a New Question
Menu

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

1 answer

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:

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