The quotient of the rational expressions shown below is 2(x + 2) / (x - 3) (Opion B)
Data obtained from the question
- (x² + 5x + 6) / (x - 6) ÷ (x² - 9) / (2x - 12)
- Quotient =?
How to determine the quotient
To determine the quotient, we shall reduce the expression to it's lowest term. This is illustrated below:
(x² + 5x + 6) / (x - 6) ÷ (x² - 9) / (2x - 12)
(x² + 5x + 6) / (x - 6) × (2x - 12) / (x² - 9)
(x² + 5x + 6) / (x - 6) × 2(x - 6) / (x² - 9)
(x² + 5x + 6) × 2 / (x² - 9)
Recall
x² + 5x + 6 = (x + 2)(x + 3)
x² - 9 = x² - 3² = (x - 3)(x + 3)
Thus,
(x² + 5x + 6) × 2 / (x² - 9) = (x + 2)(x + 3) × 2 / (x - 3)(x + 3)
(x² + 5x + 6) × 2 / (x² - 9) = 2(x + 2) / (x - 3)
Therefore, the quotient is 2(x + 2) / (x - 3)
Complete question
See attached photo
Learn more about algebra:
https://brainly.com/question/953809
#SPJ1
