Question

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

Answer 1

To divide the rational expressions (2x-3)/(5x^2) and (x-5)/(3x-1), we need to multiply the first expression by the reciprocal of the second expression:

(2x-3)/(5x^2) ÷ (x-5)/(3x-1) = (2x-3)/(5x^2) * (3x-1)/(x-5)

Now we can simplify the expression by canceling out any common factors:

(2x-3)/(5x^2) * (3x-1)/(x-5) = [(2x-3)/(5x)] * [(3x-1)/(x-5)]

= (2x-3)(3x-1) / (5x)(x-5)

Therefore, the quotient of the rational expressions (2x-3)/(5x^2) and (x-5)/(3x-1) is (2x-3)(3x-1) / (5x)(x-5).

Answer 2

`\frac{2x - 3}{5 {x}^(2) } / (x - 5)/(3x - 1) =`

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

`\frac{(2x - 3)(3x - 1)}{5 {x}^(2) (x - 5)} = \frac{6 {x}^(2) - 11x + 3}{5 {x}^(3) - 25 {x}^(2) }`