Question

Divide and state the quotient in simplest form. 36y/y²-2y+1 / 12y²/y²-1

A. (3y+3)/y²-y
B. (y(y-1))/3(y+1)
C. 3/y
D. (3(y²-1))/y(y²-2y+1)

Answer 1

To divide the given fractions, we convert the division to a multiplication by taking the reciprocal of the second fraction and then multiply straight across. After simplifying, the quotient in simplest form is 3/y, which corresponds to option C.

Step-by-step explanation:

To divide the given expression and state the quotient in simplest form, we start by changing the division to multiplication by flipping the second fraction (taking its reciprocal). The original division problem is:

(36y ÷ (y²-2y+1)) ÷ (12y² ÷ (y²-1))

Which becomes:

(36y ÷ (y²-2y+1)) × ((y²-1) ÷ 12y²)

To simplify, multiply straight across:

(36y × (y²-1)) ÷ ((y²-2y+1) × 12y²)

=(3y(y²-1)) ÷ (y(y-1)²)

We then simplify by canceling out like terms:

= 3 ÷ (y-1)

Which simplifies to:

C. 3/y