Question

PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!! What is (f/g)(x) ?

Answer 1

Answer:   $\bold{D.\ \dfrac{x+4}{x}\ where\ x \neq 0, \dfrac{2}{3}}$

Step-by-step explanation:

f(x) = 3x² + 10x - 8

g(x) = 3x² - 2x

$\dfrac{f(x)}{g(x)}=\dfrac{3x^2+10x-8}{3x^2-2x}=\dfrac{(3x-2)(x+4)}{x(3x-2)}=\dfrac{x+4}{x}$

Restriction on x: the denominator cannot be equal to zero. So,

    x(3x - 2) ≠ 0  

→  x ≠ 0     and     3x - 2 ≠ 0

                             3x       ≠ 2

                               x       $\neq \dfrac{2}{3}$