If you ever took precalculus or some other math class which covers properties of functions, you learn how to determine the domain of the function. One of the red flags to look out for is when you divide by zero. In your expression, when x = 3, the denominator is zero. Thus, the domain is every number beside 3. Unfortunately, the number you are trying to plug in (x = 3) is the only number that doesn't work in this function.
To see this first hand, you0 can graph this function on a TI-83. If you zoom in on the point of the graph at x = 3, you will see that there is a blank spot there! That is because, as stated above, there just isn't a value of the expression at x = 3.
You may say, well it looks like the answer should be 6, looking at the graph. This concept of what the answer "should be" is what limits are all about. The values of the function on the left and right of x = 3 all go towards 6 as you get closer and closer. So we say the limit as x goes to 3 is 6.
So even though it is not technically the answer, 6 is your best choice. Zero is absolutely not correct in any sense. The very best answer is to say that the expression is undefined at x = 3.
This problem illustrates why 0/0 is called indeterminate. In this problem, 0/0 in a way equals 6. The idea that 0/0 can equal anything is actually the essence of calculus.
I got an A+ in mathematical analysis in college.