A proper rational function is a rational function 
for which the polynomial degree of the numerator
is smaller than that of the denominator,
Every rational function can be written by polynomial division as a polynomial
plus a proper rational function. This form is used in partial
fraction decomposition and integration
by partial fractions.
See also
Integration by Partial Fractions,
Partial Fraction Decomposition,
Polynomial Division,
Rational
Function
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References
Stewart, J. Calculus: Early Transcendentals, 7th ed.
Belmont, CA: Brooks/Cole, 2012.
Cite this as:
Weisstein, Eric W. "Proper Rational Function."
From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ProperRationalFunction.html
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