1. www.le.ac.uk Partial Fractions Department of Mathematics University of Leicester

2. Content Quadratic factorsLinear factorsRepeated factorsIntroduction

3. Next Repeated factors Quadratic factors Linear factors Introduction

4. Linear factors The decomposition of a given fraction into partial fractions is achieved by first factorising the denominator Next Repeated factors Quadratic factors Linear factors Introduction

5. If the factors are linear then we will have partial fractions of this form Linear factors Next Repeated factors Quadratic factors Linear factors Introduction

6. Linear factors Next Repeated factors Quadratic factors Linear factors Introduction

7. Linear factors … and solving this equivalence Next Repeated factors Quadratic factors Linear factors Introduction

8. Cover-up method If we “cover-up” the factor associated with the value we want to fin and then evaluate at it’s zero we will achieve the value we were looking for. You can check this is correct with the previous method. This only works with linear factors! Next Repeated factors Quadratic factors Linear factors Introduction

9. Higher order factors Next Repeated factors Quadratic factors Linear factors Introduction If there is a quadratic factor we have partial fractions of this form.

10. Higher order factors Next Repeated factors Quadratic factors Linear factors Introduction Rearrange to gain this equivalence.

11. Higher order factors Next Repeated factors Quadratic factors Linear factors Introduction

12. Repeated factors Next Repeated factors Quadratic factors Linear factors Introduction If there is a repeated factor we have partial fractions of this form. The numerator of the linear factor was found using the cover-up method.

13. Repeated factors Next Repeated factors Quadratic factors Linear factors Introduction

14. Repeated factors Next Repeated factors Quadratic factors Linear factors Introduction

15. Summary A linear factor gives a partial fraction of the form: A quadratic factor gives a partial fraction of the form: A repeated factor gives a partial fraction of the form: Next Repeated factors Quadratic factors Linear factors Introduction