Question

Which of the following is the product of the rational expressions shown below? 3x x + 2 X-4 X + 4 3x2 + 6x O A. X – 16 O B. 3x + 2x x - 16 O c. *** 3x + 6 x2 - 16 O D. 4x + 2 x2

Answer 1

EXPLANATION

Given the rational expression:

`(x+2)/(x-4)\cdot(3x)/(x+4)`

Expanding (x+4)(x-4) and multiplying terms:

`(x+2)/(x-4)\cdot(3x)/(x+4)=(3x(x+2))/(x^2-4x+4x-16)`

Applying the distributive property:

`(3x(x+2))/(x^2-4x+4x-16)=(3x^2+6x)/(x^2-16)`

Hence, the appropiate expression is as follows:

`(x+2)/(x-4)\cdot(3x)/(x+4)=(3x^2+6x)/(x^2-16)`

The answer is the option A