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1.13 Examples of rational arithmetic

Improper rational function

For example

{{X^{2}+6X+14}\over{X+4}}.

This is improper, since the degree of the numerator is two, whereas the degree of the denominator is one. By dividing, we can write

{{X^{2}+6X+14}\over{X+4}}=X+2+{{6}\over{X+4}},

where $6/(X+4)$ is proper.