Answer:
third option
Step-by-step explanation:
[tex]\frac{g(x)}{f(x)}[/tex] = [tex]\frac{x^2}{3x+5}[/tex]
The denominator of the rational function cannot be zero as this would make the function undefined. Equating the denominator to zero and solving gives the value that x cannot be
3x + 5 = 0 ⇒ 3x = - 5 ⇒ x = - [tex]\frac{5}{3}[/tex] ← excluded value
Thus the domain of [tex]\frac{g(x)}{f(x)}[/tex] is the set of all real numbers except - [tex]\frac{5}{3}[/tex]
