Answer:
Option B. [tex]\frac{1}{3x+1}[/tex].
Step-by-step explanation:
The given expression is [tex]\frac{x+2}{x^{3}+2x^{2}-9x-18}\div \frac{3x+1}{x^{2}-9}[/tex]
In this expression we will simplify [tex]\frac{x+2}{x^{3}+2x^{2}-9x-18}[/tex] first.
=[tex]\frac{x+2}{x^{2}(x+2)-9(x+2)}[/tex]
[tex]=\frac{x+2}{(x+2)(x^{2}-9)}[/tex]
[tex]=\frac{1}{x^{2}-9}[/tex]
Now we can rewrite the given expression as
[tex]=\frac{1}{x^{2}-9}\div \frac{3x+1}{x^{2}-9}[/tex]
[tex]=\frac{1}{x^{2}-9}\times \frac{x^{2}-9}{3x+1}[/tex]
[tex]= \frac{1}{3x+1}[/tex]
So option B. [tex]\frac{1}{3x+1}[/tex] is the right answer.
