Question

Which of the following is the quotient of the rational expressions shown below?

Answer 1

We have two rational expressions. One in numerator and one in denominator.
Dividing by a fraction is equivalent to multiplying by its reciprocal. The rational expression in the denominator can be multiplied by taking its reciprocal to simplify the overall expression as shown below.

$\frac{ \frac{4x+1}{6x} }{ \frac{x}{3x-1} } \\ \\ = \frac{4x+1}{6x} * \frac{3x-1}{x} \\ \\ = \frac{(4x+1)(3x-1)}{6 x^{2} }$

There are no common factors, so the expression can be simplified any further.