What are the types of rational algebraic fractions?

Step 1
There are two types of rational algebraic fractions namely proper algebraic fractions and improper algebraic fractions.
A rational algebraic fraction ${\displaystyle \frac{f\left(x\right)}{g\left(x\right)}}$ consisting of the numerator with lower degree than the denominator is defined as proper algebraic fractions.
Example: ${\displaystyle \frac{x^2}{x^3+1}}$
Step 2
A rational algebraic fraction ${\displaystyle \frac{f\left(x\right)}{g\left(x\right)}}$ consisting of the numerator with higher degree than the denominator is defined as improper algebraic fractions.
Example: ${\displaystyle \frac{x^2+1}{x}}$