1. Definition of a Rational Fraction: A rational fraction is an expression of the form $\frac{f(x)}{g(x)}$, where $f(x)$ and $g(x)$ are polynomials and $g(x) \neq 0$.
2. Classification Criteria:
• Proper Fraction: A fraction where the degree of the numerator is strictly less than the degree of the denominator ($\deg f(x) \lt \deg g(x)$).
• Improper Fraction: A fraction where the degree of the numerator is greater than or equal to the degree of the denominator ($\deg f(x) \geq \deg g(x)$).
3. Application to the Problem: The question states that $\deg f(x) \geq \deg g(x)$. By following the mathematical definitions established above, this condition explicitly identifies the expression as an
Improper fraction.
Just like numerical fractions (e.g., $7/3$), improper rational fractions can be simplified using long division into the sum of a polynomial and a proper rational fraction.