Question 817077
The domain is in essence defined by what x cannot be. In other words the denominator cannot not equal to 0, the reason being if the number the denominator is equal to 0 the answer is undefined. So, in this case 

{{{(9x^2-36)/(x+2)}}} 

What number will make the denominator 0? 

In this case if x = 2 then the denominator will equal 0. Thus x cannot equal 2. This is also your domain.  

Now lets simplify. 

{{{ (9x^2-36) = 9 (x^2-4) }}} 

So our factor for the numerator is: 

{{{ (9)(x-2)(x+2) }}} 

Now we divide by cancelling similar terms like so: 

{{{(9)cross(x+2)(x-2)/cross(x+2)}}} 

Ultimately, our final answer is: 

{{{(9)(x-2)}}}