Question

which of the following is the quotient of the rational expressions shown below?
x-4/2x^2÷2x+3/x+4

Answer 1

ANSWER

$\frac{ {x - }^{2} - 16}{4 {x}^{3} + 6 {x}^{2} }$

EXPLANATION

The given rational expression is

$\frac{x - 4}{2 {x}^{2} } \div \frac{2x + 3}{x + 4}$

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

$\frac{x - 4}{2 {x}^{2} } \times \frac{x + 4}{2x + 3}$

The product of the numerators are difference of two squares:

When we multiply out and expand we get:

$\frac{ {x - }^{2} - 16}{4 {x}^{3} + 6 {x}^{2} }$