Final answer:
The expression 3√3 / 3√2x simplifies to √6 / 2x after dividing by the common coefficient and rationalizing the denominator.
Step-by-step explanation:
The expression given is 3√3 / 3√2x. To simplify this expression, we look to reduce the radicals and coefficients where possible. Given that there is a common coefficient of 3 in both the numerator and denominator, we can simplify by dividing both by 3. This action alone simplifies the expression to √3 / √2x.
To further simplify, we can rationalize the denominator by multiplying both the numerator and the denominator by √2, thus getting rid of the radical in the denominator.
The step of rationalizing the denominator would give us (√3 * √2) / (√2x * √2) = √6 / 2x. The final simplified form of the expression is therefore √6 / 2x, which corresponds to option B.