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3 years ago

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

Mathematics

1 answer:

Rudiy273 years ago

8 0

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

<u>Step-by-step explanation:</u>

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

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