Written in simplest form,
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)
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
actually, that's x ≠ -3y, but it does not affect the final answer.
Just sayin' ...
To simplify the given expression, we can start by factoring out the greatest common factor from both the numerator and denominator. In this case, the GCF is 3xy.
Numerator:
3x^3 - 27xy^2
= 3xy(x^2 - 9y^2)
Denominator:
12x^2 + 36xy
= 12x(x + 3y)
Now, we can cancel out the common factor of 3xy from the numerator and the denominator:
= (3xy(x^2 - 9y^2)) / (3xy∙4(x + 3y))
Next, we simplify the expression further:
= (x^2 - 9y^2) / (4(x + 3y))
Therefore, the simplified form of the expression is (x^2 - 9y^2) / (4(x + 3y)).
Out of the given options, none of them match exactly. However, if we rewrite the expression as (x^2 - 9y^2) / (4)(x + 3y), it can be considered similar to option (4): x - 3y / 4(x + 3y).