SOLUTION
What is the quotient of the rational expression shown below:
[tex]\frac{x^2+5x+6}{x-6}\div\frac{x^2-9}{2x-12}[/tex][tex]\begin{gathered} \frac{x^2+5x+6}{x-6}\times\frac{2(x-6)}{x^2-9} \\ \frac{x^2+3x+2x+6}{x-6}\times\frac{2(x-6)}{x^2-3^2} \\ \frac{x(x+3)+2(x+3)}{\cancel(x-6)}\times\frac{2\cancel(x-6)}{(x+3)(x-3)} \\ \frac{(x+3)(x+2)}{1}\times\frac{2}{(x+3)(x-3)} \end{gathered}[/tex][tex]\begin{gathered} \frac{\cancel(x+3)(x+2)}{1}\times\frac{2}{(x-3)\cancel(x+3)} \\ \frac{2(x+2)}{x-3} \end{gathered}[/tex][tex]\frac{2(x+2)}{x-3}[/tex]
Final answer = Option A
