Question

Simplify the expression given below. x+2/X^3+2x^2-9x-18 divided by 3x +1/x^2-9

Answer 1

Answer:

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

Explanation:

1) Expression given:

$\frac{ \frac{x+2}{x^3+2x^2-9x-18} }{ \frac{3x+1}{x^2-9} }$

2) Factor the denominator of the first fraction:

$x^3+2x^2-9x-18=(x^3+2x^2)-(9x+18)=x^2(x+2)-9(x+2)=$

$(x+2)(x^2-9)$

3) Rewrite the expression

$\frac{ \frac{x+2}{(x+2)(x^2-9)} }{ \frac{3x+1}{x^2-9} }$

4) In the upper fraction x+2 in the numerator cancels out with x + 2 in the denominator.

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

5) x² - 9 in both denominators cancel out each other, and the final result is:

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