Answer:
(D)[tex]\frac{x(x+3)}{x+1}[/tex]
Step-by-step explanation:
Given are the functions:
[tex]f(x)=x^{3}-9x[/tex] and [tex]g(x)=x^{2}-2x-3[/tex].
Applying the operations on the given functions, we get
[tex]\frac{f(x)}{g(x)}=\frac{x^{3}-9x}{x^{2}-2x-3}[/tex]
=[tex]\frac{x(x^{2}-9)}{x^{2}-3x+x-3}[/tex]
=[tex]\frac{x(x+3)(x-3)}{x(x-3)+1(x-3)}[/tex]
=[tex]\frac{x(x+3)(x-3)}{(x+1)(x-3)}[/tex]
=[tex]\frac{x(x+3)}{x+1}[/tex]
Thus, [tex]\frac{f(x)}{g(x)}[/tex]=[tex]\frac{x(x+3)}{x+1}[/tex]
Hence, option D is correct.
