Written in simplest form,

Question

3x^3-27xy^2 / 12x^2+36xy is:
(1) x+3y/4
(2) x+4y/3
(3) x-3y/4
(4) x-3y/4(x+3y)

My work:
3x^327xy^2/12x^2+36xy=3x(x^2-9y^2/3x(4x+12y)=x^2-9y^2/4(x+3y)

Answer 1

you did not finish at the end

3x(x^2-9y^2/(3x(4x+12y)) is correct, notice the brackets at the denominator

= 3x(x-3y)(x+3y)/((3x)(4)(x+3y))
= (x-3y)/4 , x ≠ 3y

looks like choice #1, if you had included the brackets

Answer 2

actually, that's x ≠ -3y, but it does not affect the final answer.

Just sayin' ...