The reason why it is undefined is as follows:
Any value for x that you chose ( provided x is a real number ) will satisfy that equation. Therefore, when considering what value to assign "0/0" we are left only with the ability to chose a value arbitrarily. In other words, no value for 0/0 makes anymore sense than any other. This is what is referred to as "Indeterminate"
Now, consider:
In this case, we have a real difficulty, because for any finite x, 0*x = 0 which is ( for obviously important reasons ) not 3! So if you wanted to say that 3/0 was "10" ( for example ), you would be saying that 0*10 = 3. So clearly, 3/0 can't be any finite number.
Additionally, consider the function f(x) = 1/x, for |x| very small ( | | is absolute value, or magnitude ), in other words, x is very close to 0. If x is negative and close to 0, then f(x) is negative and very large ( in a magnitude sense ). If x is positive and close to 0, then f(x) is positive and very large. This would indicate that simply saying "1/0 is infinity" has its own problems, namely: it could be positive or negative infinity, and we have no reason to chose one over the other. For this reason ( namely, 0x = 3 having no solutions in the finite, and having serious difficulties in the transfinite ), we simply say "Division by 0 is undefined", which can be thought of as saying: "Any choice for it's value is just wrong".

It may interest you to know, however, that there are certain situations in which division by 0, and infinity become semi-acceptable to talk about, but unforunately, this is not the case with the normal situation ( such as working with "Real Numbers", for example )

Hope this clarifies the issue for you,

-joeboo