Question

What is the quotient? startfraction 2 y squared minus 6 y minus 20 over 4 y 12 endfraction divided by startfraction y squared 5 y 6 over 3 y squared 18 y 27 endfraction startfraction 2 over 3 (y minus 5) endfraction startfraction 3 (y minus 5) over 2 endfraction startfraction (y minus 5) (y 2) squared over 6 (y 3) squared endfraction startfraction 3 (y 5) (y minus 2) over 2 (y 2) endfraction

Answer 1

The quotient of two fractions, (2y² - 6y - 20)/(4y + 12) and (y² + 5y + 6)/(3y² + 18y + 27), is: 3(y - 5)/2

What is a Quotient?

Quotient can be described as the result you get from dividing a term by another term.

Let's find the quotient of (2y² - 6y - 20)/(4y + 12) and (y² + 5y + 6)/(3y² + 18y + 27)

Quotient = (2y² - 6y - 20)/(4y + 12) ÷ (y² + 5y + 6)/(3y² + 18y + 27)

Change the division sign to multiplication sign and turn the second fraction upside down

(2y² - 6y - 20)/(4y + 12) × (3y² + 18y + 27)/(y² + 5y + 6)

Bringing out the common terms, we would have:

2(y² - 3y - 10)/4(y + 3) × 3(y² + 6y + 9)/(y² + 5y + 6)

Factorize

2(y - 5)(y + 2)/4(y + 3) × 3(y + 3)(y + 3)/(y + 3)(y + 2)

Cancel out common factors

= 3(y - 5)/2

Quotient = 3(y - 5)/2

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