Question

F(x)=2x^2+4x-16 g(x)=4x^2-16 Find (f/g)(x).

Answer 1

Answer:

Step-by-step explanation:

$(\frac{f}{g} )(x) = \frac{2x^{2} +4x-16}{4x^{2} -16}$

2x²+4x -16 =  2(x²+2x-8); factor 2

                  = 2(x+4)(x-2) ;factor the quadratic equation

4x²-16  = 4(x²-4) ; factor 4

            =4(x²- 2²) ; rewrite 4 as 2²

           = 4(x-2)(x+2); now use the difference of two squares a²-b²=(a-b)(a+b)

so now we have:

$(\frac{f}{g}) (x) = \frac{2(x+4)(x-2)}{4(x-2)(x+2)}$ ; simplify (x-2) from numerator and denominator

                                  and 2/4 as 1/2

$(\frac{f}{g}) (x) = \frac{(x+4)}{2(x+2)}$