It is often helpful to break down a complicated algebraic fraction into a sum of simpler fractions. For example it can be shown that has the same value as for any value of . We say that
and that the partial fractions of are and .
The ability to express a fraction as its partial fractions is particularly useful in the study of Laplace transforms, -transforms, Control Theory and Integration. In this Section we explain how partial fractions are found.
- be familiar with addition, subtraction, multiplication and division of algebraic fractions
- distinguish between proper and improper fractions
- express an algebraic fraction as the sum of its partial fractions
2 Proper fractions with linear factors
3 Proper fractions with repeated linear factors
4 Proper fractions with quadratic factors
5 Engineering Example 3
6 Improper fractions