Nice video. Interesting that you put each result above the highest-power current term (t^{2} above t^{3}, e.g.) instead of the corresponding power term (t^{2} above t^{2}, e.g.). Also, for novices, if there are missing terms in the divisor then it helps to expand it w/ 0 coefficients also, although in this example that is not needed, and of course with the familiarity of practice it isn't even necessary.

The one big point that I always drive home with students is that performing this division doesn't change the function at all - it's just two different representations of the exact same function, just like 1/2 and 0.5 are two different representations of the same number. In other words, you get exactly the same results whether you plug a value into the original rational function or into one you obtain as a result of the division, and the graphs of both equations are identical. This becomes very useful, for example, when discussing slant asymptotes as the final term can be interpreted as the difference between the slant asymptote and the actual graph.

## Comments

^{2}above t^{3}, e.g.) instead of the corresponding power term (t^{2}above t^{2}, e.g.). Also, for novices, if there are missing terms in the divisor then it helps to expand it w/ 0 coefficients also, although in this example that is not needed, and of course with the familiarity of practice it isn't even necessary.