How do I divide (12x^3 +2y)/(2x+4y^3)?

boy, there's not much to do there. You can factor out a 2, but that just gives you

(6x^3+y)/(x+2y^3)

which you can't massage much. Long division just gives you

6x^2 - 12xy^3 + 24y^6 + (y-48y^9)/(x+2y^3)

Is there something else involved here?

yes it is above this question. x(12x^3 +2y)/y(2x+4y^3)

from x/y = (6x^3+y)/(x+2y^3)

Not much help. It still doesn't lend itself to any kind of algebraic manipulation. The numeric solutions are along the lines of

x = ±0.4683
y = ±0.2684, ±1.4156

To divide the expression (12x^3 + 2y) by (2x + 4y^3), follow these steps:

Step 1: Determine if the expression is factorable.
In this case, both terms in the numerator and the denominator are already in their simplest form and cannot be factored further.

Step 2: Apply long division.
Write the expression in long division format. Place the dividend (12x^3 + 2y) inside the division bracket and the divisor (2x + 4y^3) outside the bracket:

_______
2x + 4y^3 | 12x^3 + 2y

Step 3: Divide the first term.
Divide the first term of the dividend (12x^3) by the first term of the divisor (2x). The result becomes the quotient's first term:

_______
2x + 4y^3 | 12x^3 + 2y
- (6x^2)

Step 4: Multiply and subtract.
Multiply the result from step 3 (6x^2) with the entire divisor (2x + 4y^3) and subtract it from the dividend (12x^3 + 2y):

_______
2x + 4y^3 | 12x^3 + 2y
- (6x^2 + 12xy^2)
_________________
-6xy^2 + 2y

Step 5: Repeat the process.
Repeat steps 3 and 4 with the new expression (-6xy^2 + 2y) as the new dividend:

_______
2x + 4y^3 | 12x^3 + 2y
- (6x^2 + 12xy^2)
_________________
-6xy^2 + 2y
+ (3y)

Step 6: Finalize the quotient.
Repeat step 3 and 4 with the new expression (3y) as the new dividend:

_______
2x + 4y^3 | 12x^3 + 2y
- (6x^2 + 12xy^2)
_________________
-6xy^2 + 2y
+ (3y)
___________
-y

Step 7: Write the final quotient.
The final quotient is -6x^2 - 6xy^2 + 3 - (y / (2x + 4y^3)).