What is the product? 2y/y-3 x 4y - 12/2y+8

4y / (y+4)

Step-by-step explanation:

2y / (y-3) x [ (4y - 12) / (2y+8) ]

To determine this, at first we have to break the parentheses. Since there is no matching values, we have to multiply the numerators and denominators.

[2y x (4y - 12) ] / (y-3) x (2y + 8)

or, [ (2y*4y) - (2y*12) ]/[ (y*2y) + (y*8) - (3*2y) - (3*8) ]

(using algebraic equation)

or, (8y^2 - 24y) / (2y^2 + 8y - 6y - 24)

or, (8y^2 - 24y) / (2y^2 + 2y - 24)

or, 8y (y - 3) / 2 (y^2 + y - 12) (taking common)

or, 4y (y - 3) / (y^2 + 4y - 3y - 12)

or, 4y (y - 3) / [y (y + 4) - 3 (y + 4) ] (Using factorization or Middle-Term factor)

or, 4y (y - 3) / (y + 4) (y - 3)

or, 4y / (y + 4) [as (y-3) / (y-3) = 1, we have dropped the part]

The answer is = 4y / (y+4)