Answer:
The LCD of the two given fraction is (x + 4)(x + 5)(x + 7)
Explanation:
In the algebraic fractions, the LCD is the least common denominator to find it do that:
- Factorize each denominator
- Take all the factors without repeating factors
Let us do that with our question
∵ The denominator of the first fraction is m² + 9m + 20
→ Factorize it into two factors
∵ 20 = 4 × 5 ⇒ the last term
∵ 4 + 5 = 9 ⇒ the coefficient of the middle term
∴ m² + 9m + 20 = (x + 4)(x = 5)
∴ The factors of m² + 9m + 20 are (x + 4) and (x + 5)
Do the same with the 2nd denominator
∵ The denominator of the second fraction is m² + 11m + 28
→ Factorize it into two factors
∵ 28 = 4 × 7 ⇒ the last term
∵ 4 + 7 = 11 ⇒ the coefficient of the middle term
∴ m² + 11m + 28 = (x + 4)(x + 7)
∴ The factors of m² + 11m + 28 are (x + 4) and (x + 7)
∵ The factors of the two denominators are (x + 4), (x + 5), (x + 4), (x + 7)
→ LCD will be all factors without repeating which means we will
take the factor (x + 4) just one time, we will not repeat it.
∴ LCD = (x + 4)(x + 5)(x + 7)
∴ The LCD of the two given fraction is (x + 4)(x + 5)(x + 7)