Question

Which of the following is the quotient of the rational expressions shown below? 2x-3/5x^2 divided by x-5/3x-1

Answer 1

Find the attachment bellow.

First, form the expression.

(2x-3)/(5x²) ÷ (x-5)/(3x-1)

= (2x-3)/(5x²) ×(3x-2)/(x-5)

 = ((2x-3)(3x-1))/((5x²)(x-5))

= (6x²-11x+3)/(5x³-25x²)

Answer 2

The expression in fraction form will be:

$\frac{ \frac{2x-3}{5 x^{2} } }{ \frac{x-5}{3x-1} }$

The denominator can be multiplied to the numerator by taking its reciprocal as shown below:

$\frac{2x-3}{5 x^{2} } * \frac{3x-1}{x-5} \\ \\ = \frac{(2x-3)(3x-1)}{5 x^{2}(x-5) }$

There are no common factors, so the expression can not be simplified any further.