What is the result of simplifying the expression 2x³ + 6x / 3x?

To simplify the expression ( \frac{2x^3 + 6x}{3x} ), you first need to factor the numerator. The numerator ( 2x^3 + 6x ) can be factored by taking out the common factor, which is ( 2x ).

This gives us: [

2x(x^2 + 3) ]

Now, the expression can be rewritten using this factorization: [ \frac{2x(x^2 + 3)}{3x} ]

Next, you can cancel out the ( x ) in the numerator and the denominator, assuming ( x \neq 0 ). This simplifies to: [ \frac{2(x^2 + 3)}{3} ]

Now, placing this expression back into a format allows us to express it as: [ \frac{2}{3}(x^2 + 3) ]

This shows that the final simplified form of the original expression is ( \frac{2}{3}(x^2 + 3) ). Therefore, this is why the correct choice reflects this simplification process.