Question

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Answer 1

Answer:

The LCD of the two given fraction is (x + 4)(x + 5)(x + 7)

Step-by-step 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)