Questions: Which of the tollowing is the quotient of the rational expressions shown below? Make sure your answer is in reduced form. (3x-6)/(x^3) ÷ (x-2)/(2x-1) A. (4x-8)/(x^3+2x-1) B. (3x^2-12x+12)/(2x^4-x^3) C. (6x^2-15x+6)/(x^4-2x^3) D. (5x-7)/(x^3+x-2) E. (6x-3)/(x^3)

Determine the quotient of the rational expressions $\frac{3x - 6}{x^3} \div \frac{x - 2}{2x - 1}$.

Rewrite the division as multiplication.

The expression can be rewritten as $\frac{3x - 6}{x^3} \times \frac{2x - 1}{x - 2}$.

Factor the numerator and denominator.

The numerator $3x - 6$ factors to $3(x - 2)$, and the denominator $x^3$ remains as is. Thus, we have: $$\frac{3(x - 2)}{x^3} \times \frac{2x - 1}{x - 2}$$

Cancel common factors.

The $(x - 2)$ in the numerator and denominator cancels out, resulting in: $$\frac{3(2x - 1)}{x^3}$$

The simplified result is $\boxed{\frac{3(2x - 1)}{x^3}}$.

Identify the final simplified expression.

Present the simplified expression.

The final simplified expression is $\frac{3(2x - 1)}{x^3}$.

Compare with the provided options.

The expression $\frac{3(2x - 1)}{x^3}$ does not match any of the provided options directly, but can be expressed as $\frac{6x - 3}{x^3}$ by distributing the 3 in the numerator.

The closest match is $\boxed{\frac{6x - 3}{x^3}}$.

The simplified result of the quotient is $\boxed{\frac{3(2x - 1)}{x^3}}$.
The closest match to the simplified expression is $\boxed{\frac{6x - 3}{x^3}}$.