Question

Need help with this math question

Answer 1

(D)
`(x(x+3))/(x+1)`

Explanation:

Given are the functions:

`f(x)=x^(3)-9x` and
`g(x)=x^(2)-2x-3`.

Applying the operations on the given functions, we get

`(f(x))/(g(x))=(x^(3)-9x)/(x^(2)-2x-3)`

=
`(x(x^(2)-9))/(x^(2)-3x+x-3)`

=
`(x(x+3)(x-3))/(x(x-3)+1(x-3))`

=
`(x(x+3)(x-3))/((x+1)(x-3))`

=
`(x(x+3))/(x+1)`

Thus,
`(f(x))/(g(x))`=
`(x(x+3))/(x+1)`

Hence, option D is correct.