ANSWER
[tex]( \frac{f}{g} )(x) = \frac{1}{3} ( {x}^{2} + 3x + 9)[/tex]
EXPLANATION
The given functions are
[tex]f(x) = {x}^{3} - 27[/tex]
and
[tex]g(x) = 3x - 9[/tex]
[tex]( \frac{f}{g} )(x) = \frac{f(x)}{g(x)} [/tex]
[tex]( \frac{f}{g} )(x) = \frac{ {x}^{3} - 27}{3x - 9} [/tex]
[tex]( \frac{f}{g} )(x) = \frac{ (x - 3)( {x}^{2} + 3x + 9) }{3(x -3 )} [/tex]
Cancel the common factors,
[tex]( \frac{f}{g} )(x) = \frac{ {x}^{2} + 3x + 9 }{3} [/tex]
OR
[tex]( \frac{f}{g} )(x) = \frac{1}{3} ( {x}^{2} + 3x + 9)[/tex]
