Answer:
Step-by-step explanation:
[tex](\frac{f}{g} )(x) = \frac{2x^{2} +4x-16}{4x^{2} -16}[/tex]
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:
[tex](\frac{f}{g}) (x) = \frac{2(x+4)(x-2)}{4(x-2)(x+2)}[/tex] ; simplify (x-2) from numerator and denominator
and 2/4 as 1/2
[tex](\frac{f}{g}) (x) = \frac{(x+4)}{2(x+2)}[/tex]
