EXPLANATION
Given the rational expression:
[tex]\frac{x+2}{x-4}\cdot\frac{3x}{x+4}[/tex]Expanding (x+4)(x-4) and multiplying terms:
[tex]\frac{x+2}{x-4}\cdot\frac{3x}{x+4}=\frac{3x(x+2)}{x^2-4x+4x-16}[/tex]Applying the distributive property:
[tex]\frac{3x(x+2)}{x^2-4x+4x-16}=\frac{3x^2+6x}{x^2-16}[/tex]Hence, the appropiate expression is as follows:
[tex]\frac{x+2}{x-4}\cdot\frac{3x}{x+4}=\frac{3x^2+6x}{x^2-16}[/tex]The answer is the option A
