In this video I cover how to decompose improper fractions. Improper fractions are fractions where the degree (or the highest power) of the denominator is smaller than or equal to the degree of the numerator. For improper fractions the techniques used in my earlier videos on proper fractions don't apply but we can first break down improper fractions to proper fractions by performing polynomial long division.
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Partial Fraction Decomposition: Improper Fractions
In my earlier videos on partial fraction decomposition, I covered cases where the denominator of the rational function had a higher "degree" than the numerator:
When the degree of the denominator is larger than the degree of the numerator, it is called a "proper" fraction.
When the degree of the denominator is smaller or equal to the degree of the numerator, it is a called an "improper" fraction. This definition is the same for basic fractions:
Partial fraction decomposition only works for proper fractions so for improper fractions we first need to use polynomial long division (see my earlier videos in description) to initially break down the fraction which will yield a remainder. For example consider the following:
