Question

Simplify the expression given below.

X+2/x^3+2x^2-9x-18 divided by 3x+1 / x^2-9

A. 1 / (x+3)(x-3)
B. 3x +1
C. 1 / 3x+1
D. 3x + 1 / (x+3) (x-3)

Answer 1

D

Step-by-step explanation: your welcome have a good day

Answer 2

C.
`(1)/(3x + 1)`

Explanation:

`(x + 2)/(x^3 + 2x^2 - 9x - 18) / (3x + 1)/(x^2 - 9) =`

Factor all polynomials.

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

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

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

To divide by a fraction, multiply by its reciprocal.

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

Cancel out common factors in the numerator and denominator.

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