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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)

Simplify The Expression Given Below X2x32x29x18 Divided By 3x1 X29 A 1 X3x3 B 3x 1 C 1 3x1 D 3x 1 X3 X3 class=

Sagot :

Answer:

D

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

mathstudent55

Answer:

C.  [tex] \dfrac{1}{3x + 1} [/tex]

Step-by-step explanation:

[tex] \dfrac{x + 2}{x^3 + 2x^2 - 9x - 18} \div \dfrac{3x + 1}{x^2 - 9} = [/tex]

Factor all polynomials.

[tex] = \dfrac{x + 2}{x^2(x + 2) -9(x + 2)} \div \dfrac{3x + 1}{(x + 3)(x - 3)} [/tex]

[tex] = \dfrac{x + 2}{(x^2 - 9)(x + 2)} \div \dfrac{3x + 1}{(x + 3)(x - 3)} [/tex]

[tex] = \dfrac{x + 2}{(x + 3)(x - 3)(x + 2)} \div \dfrac{3x + 1}{(x + 3)(x - 3)} [/tex]

To divide by a fraction, multiply by its reciprocal.

[tex] = \dfrac{x + 2}{(x + 3)(x - 3)(x + 2)} \times \dfrac{(x + 3)(x - 3)}{3x + 1} [/tex]

Cancel out common factors in the numerator and denominator.

[tex] = \dfrac{1}{3x + 1} [/tex]

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