Question

Divide and simplify

(3y-6)/14÷(y-2)/4y

I think I am supposed to multiply both sides by 4y. Help.

Answer 1

(3y - 6) / 14 + (y - 2) / 4y ,
Find a common denominator:
(6y^2 - 12y + 7y - 14) / 28y,
Combine like-terms:
(6y^2 - 5y - 14) / 28y,

Answer 2

(3y - 6) / 14 + (y - 2) / 4y ,
Find a common denominator:
(6y^2 - 12y + 7y - 14) / 28y,
Combine like-terms:
(6y^2 - 5y - 14) / 28y,
Use A*C Method to factor numerator:
A*C = 6 * -14 = -84 = 7 * -12,
6y^2 + (7y - 12y) - 14,
Group the 4 terms into 2 factorable pairs:

(6y^2 - 12y) + (7y - 14),
6y(y - 2) + 7(y - 2),
(y - 2) (6y + 7) / 28y.