Question

Given f (x)=2x-5x-3 and g (x)=2x^2+x what is (f/g)(x)​

Answer 1

ANSWER

$( \frac{f}{g} )(x ) = \frac{x - 3}{x} \: where \: \: x \ne0, - \frac{1}{2}$

EXPLANATION

Given:

$f(x) = 2 {x}^{2} - 5x - 3$

and

$g(x) = 2 {x}^{2} + x$

Then,

$( \frac{f}{g} )(x ) = \frac{f(x)}{g(x)}$

Substitute the given functions;

$( \frac{f}{g} )(x ) = \frac{2 {x}^{2} - 5x - 3}{2 {x}^{2} + x}$

Factor

$( \frac{f}{g} )(x ) = \frac{2 {x}^{2} - 6x + x - 3 }{x(2x + 1)}$

$( \frac{f}{g} )(x ) = \frac{2x(x - 3) +1 (x - 3)}{x(2x + 1)}$

$( \frac{f}{g} )(x ) = \frac{(2x + 1)(x - 3) }{x(2x + 1)}$

Cancel the common factors.

$( \frac{f}{g} )(x ) = \frac{x - 3}{x} \: where \: \: x \ne0, - \frac{1}{2}$