Question

Simplify the expression given below.

Answer 1

Answer:

Option B. $\frac{1}{3x+1}$.

Step-by-step explanation:

The given expression is $\frac{x+2}{x^{3}+2x^{2}-9x-18}\div \frac{3x+1}{x^{2}-9}$

In this expression we will simplify $\frac{x+2}{x^{3}+2x^{2}-9x-18}$ first.

=$\frac{x+2}{x^{2}(x+2)-9(x+2)}$

$=\frac{x+2}{(x+2)(x^{2}-9)}$

$=\frac{1}{x^{2}-9}$

Now we can rewrite the given expression as

$=\frac{1}{x^{2}-9}\div \frac{3x+1}{x^{2}-9}$

$=\frac{1}{x^{2}-9}\times \frac{x^{2}-9}{3x+1}$

$= \frac{1}{3x+1}$

So option B. $\frac{1}{3x+1}$ is the right answer.