Question

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

x-4/2x^2÷2x+3/x+4

Answer 1

Explanation:

Answer 2

`\frac{ {x - }^(2) - 16}{4 {x}^(3) + 6 {x}^(2) }`

EXPLANATION

The given rational expression is

`\frac{x - 4}{2 {x}^(2) } / (2x + 3)/(x + 4)`

We multiply by the reciprocal of the second function to get:

`\frac{x - 4}{2 {x}^(2) } * (x + 4)/(2x + 3)`

The product of the numerators are difference of two squares:

When we multiply out and expand we get:

`\frac{ {x - }^(2) - 16}{4 {x}^(3) + 6 {x}^(2) }`