Section 7.4 - Partial Fractions

Essential Question(s): 

Explain the skills necessary to decompose a rational function into partial fractions.

---

---

Follow these three steps to complete this "flip" lesson.

STEP 1: Preparation 
Title your spiral with the heading above and copy the essential question(s).

STEP 2: Vocabulary & Examples 
Copy and define the following of vocabulary. This can be any tables, properties, theorems, terms, phrases or postulates listed. Review the following examples and copy what is necessary for you. Use the guiding questions for your cornell notes.

Partial Fraction Decomposition

1. What is a partial fraction and partial fraction decomposition? (pg 608)
2. How do you write the decomposition factors? (Ex 1 pg 608)

Denominators with Linear Factors

1. How do you decompose a fraction with distinct linear factors? (Ex 2 pg 609-610) ***They use matrices to solve. You will use algebraic methods to solve the system.***
2. How do you decompose a fraction with a repeated linear factor? (Ex 3 pg 610)***They use matrices to solve. You will use algebraic methods to solve the system.***

Denominators with Irreducible Quadratic Factors

1. How do you decompose a fraction with an irreducible quadratic factor? (Ex 4 pg 611-612)***They use matrices to solve. You will use algebraic methods to solve the system.***
2. How do you decompose a fraction with a repeated irreducible quadratic factor? (Ex 5 pg 612)***They use matrices to solve. You will use algebraic methods to solve the system.***

Applications

1. How does partial fraction decomposition get used with investigating the graph of a rational function? (Ex 6 pg 613)

STEP 3: Reading
Read the following page(s) and take any extra notes as needed.

• Read pages 608 - 613.
• Make sure to read the paragraphs between the examples.

---

Partial Fractions