Final answer:
To divide rational expressions, multiply the first expression by the reciprocal of the second expression. The quotient of the given rational expressions is 2/(3x-1)(x-2).
Step-by-step explanation:
To divide rational expressions, we need to multiply the first expression by the reciprocal of the second expression. In this case, the quotient of the given rational expressions, x/(3x-1) divided by (x-2)/(2x) is obtained by multiplying the first expression by the reciprocal of the second expression.
Reciprocal of (x-2)/(2x) is (2x)/(x-2). So, the quotient can be written as (x/(3x-1)) * ((2x)/(x-2)).
Simplifying this expression, we can cancel out the common terms: x in the numerator of the first expression and 2x in the denominator of the second expression. Therefore, the quotient simplifies to: 2/(3x-1)(x-2).