Question

Which of the following is the quotient of this rational expression

Answer 1

(2x - 1) / 3x.

Explanation:

2x - 1 / (x + 1) / 3x^2 / (x^2 + x)

Invert the second fraction and multiply:

= (2x - 1) / (x + 1) * (x^2 + x) / 3x^2

= (2x - 1 ) / (x + 1) * x(x + 1) / 3x^2

= x(x + 1)(2x - 1) / 3x^2(x + 1)

x(x + 1) is common to top and bottom of the fraction so we divide both be x(x + 1) to give:

(2x - 1) / 3x (answer).

Answer 2

A

Explanation:

Factor, where possible the numerators/ denominators

x² + x = x(x + 1) ← common factor of x

We can express the division as multiplication by leaving the first fraction and turning the second fraction upside down, that is

`(2x-1)/(x+1)` ×
`(x(x+1))/(3x^2)`

Cancel the factor x and x + 1 on the numerator/denominator leaving

`(2x-1)/(3x)` → A