Inverse Laplace TransformsPrerequisite KnowledgeMethod of Partial FractionsDefinition: Partial FractionsDefinition: Distinct Linear FactorsDefinition: Distinct Quadratic FactorsDefinition: Repeated Linear FactorDefinition: Repeated Quadratic FactorsPracticeUse Technology to Factor ExpressionsUse Technology to Verify Partial FractionsCC BY-NC-SA 4.0

**Author**: John J Weber III, PhD
**Corresponding Textbook Sections**:

**Section 7.4**– Inverse Laplace Transforms

Rational expressions can be written as a sum of simpler fractions called **partial fractions**.

Let be a rational function where\newline and is factorable into **distinct** linear factors. Then

Let be a rational function where and is factorable into **distinct** quadratic factors. Then

Let be a rational function where\newline and is factorable into -**repeated** linear factors, i.e., . Then

Let be a rational function where and is factorable into -**repeated** quadratic factors, i.e., . Then

Rewrite the following rational expressions into a sum of partial fractions:

**Mathematica**

`1``(* Practice 01: Factor x^2-3x-4 *)`

2`Factor[x^2-3x-4]`

**Mathematica**

`xxxxxxxxxx`

21`(* Practice 01: Find partial fractions for 1/(x^2-3x-4) *)`

2`Apart[1/(x^2-3x-4)]`

**Warnings**:

- Be very
**careful**with the*syntax*.*Syntax*is the set of rules on how to write computer code. Every software program has its own unique syntax. Some basic*Mathematica*syntax is located at: http://www.jjw3.com/TECH_Common_Functions.pdf. - To execute code (including comment codes), press and hold the SHIFT key and press the ENTER key.

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**Last Modified**: Sunday, 8 November 2020 18:39 EDT