I was graphing a function today and was wondering why you devide the exponent on the highest degree on top by the exponent on the highest degree on the bottom to get the horizontal asymptote if the degrees are equal in numerator and denominator...

I understand that this works and that we can get the asymptote quite easily but the question is WHY WHY WHY??

For example, the asymptote of 2x^2+1/ 3x^2+2 would be 2/3. Why is this???