Question

Simplify the expression given below.

Answer 1

Option B.
`(1)/(3x+1)`.

Explanation:

The given expression is
`(x+2)/(x^(3)+2x^(2)-9x-18)/ (3x+1)/(x^(2)-9)`

In this expression we will simplify
`(x+2)/(x^(3)+2x^(2)-9x-18)` first.

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

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

`=(1)/(x^(2)-9)`

Now we can rewrite the given expression as

`=(1)/(x^(2)-9)/ (3x+1)/(x^(2)-9)`

`=(1)/(x^(2)-9)* (x^(2)-9)/(3x+1)`

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

So option B.
`(1)/(3x+1)` is the right answer.