# A friend emails you the results of a

- Slides: 32

A friend e-mails you the results of a recent high school swim meet. The e-mail states that 24 individuals placed, earning a combined total of 53 points. First place earned 3 points, second place earned 2 points, and third place earned 1 point. There were as many first-placed finishers as second-and third -place finishers combined. 1) Write a system of three equations that represents how many people finished in each place. 2) How many swimmers finished in first place, second place, and third place?

Day 144/145 4/19/16 7. 3 Partial Fractions Objectives: Decompose rational functions Assignment: Hand out

Warm Up Add the rational function.

The Partial Fraction Decomposition of a Rational Expression with Distinct Linear Factors in the Denominator

Example: Partial Fraction Decomposition with Distinct Linear Factors Find the partial fraction decomposition of Step 1 Set up the partial fraction decomposition with the unknown constants.

Example: Partial Fraction Decomposition with Distinct Linear Factors (continued) Find the partial fraction decomposition of Step 2 Multiply both sides of the resulting equation by the least common denominator.

Example: Partial Fraction Decomposition with Distinct Linear Factors (continued) Find the partial fraction decomposition of Step 3 Choose values for x that make the factor zero and solve the resulting equation.

Example: Partial Fraction Decomposition with Distinct Linear Factors (continued) Find the partial fraction decomposition of Step 4 Substitute values of A and B and write the partial fraction decomposition.

Example: Partial Fraction Decomposition with Distinct Linear Factors Find the partial fraction decomposition of

Example: Partial Fraction Decomposition with Distinct Linear Factors Find the partial fraction decomposition of

Find the partial fraction decomposition of

The Partial Fraction Decomposition of Has Repeated Linear Factors

Example: Partial Fraction Decomposition with Repeated Linear Factors Find the partial fraction decomposition of Step 1 Set up the partial fraction decomposition with the unknown constants.

Example: Partial Fraction Decomposition with Repeated Linear Factors (continued) Find the partial fraction decomposition of Step 2 Multiply both sides of the resulting equation by the least common denominator.

Example: Partial Fraction Decomposition with Repeated Linear Factors (continued) Find the partial fraction decomposition of Step 3 Choose values for x that make the factor zero and solve the resulting equation. How do we solve for B?

Example: Partial Fraction Decomposition with Repeated Linear Factors (continued) Find the partial fraction decomposition of Step 4 Substitute the values (A, B, or C) you have solved for and a choose a new value for x.

Example: Partial Fraction Decomposition with Repeated Linear Factors (continued) Find the partial fraction decomposition of Step 5 Substitute values of A and B and write the partial fraction decomposition.

Example: Partial Fraction Decomposition with Repeated Linear Factors Find the partial fraction decomposition of

Example: Partial Fraction Decomposition with Repeated Linear Factors Find the partial fraction decomposition of

Example: Partial Fraction Decomposition with Repeated Linear Factors Find the partial fraction decomposition of

The Partial Fraction Decomposition of a Rational Expression with Prime, Nonrepeated Quadratic Factors in the Denominator

Example: Partial Fraction Decomposition Find the partial fraction decomposition of Step 1 Set up the partial fraction decomposition with the unknown constants.

Example: Partial Fraction Decomposition (continued) Find the partial fraction decomposition of Step 2 Multiply both sides of the resulting equation by the least common denominator.

Example: Partial Fraction Decomposition (continued) Find the partial fraction decomposition of Step 3 Choose values for x that make the factor zero and solve the resulting equation. Now what do we do?

Example: Partial Fraction Decomposition (continued) Find the partial fraction decomposition of Step 4 Substitute the values (A, B, or C) you have solved for and choose x to be zero.

Example: Partial Fraction Decomposition (continued) Find the partial fraction decomposition of Step 5 Substitute the values (A, B, or C) you have solved for and choose a new value for x.

Example: Partial Fraction Decomposition (continued) Find the partial fraction decomposition of Step 6 Substitute values of A and B and write the partial fraction decomposition.

Example: Partial Fraction Decomposition Find the partial fraction decomposition of

Example: Partial Fraction Decomposition Find the partial fraction decomposition of

- A friend emails you the results
- Hello my friend friend of a friend
- Hello my friend
- Let's be a good friend
- Foaf a matic
- A friend in needs a friend indeed
- I've found a friend oh such a friend
- Writing an email to a teacher
- Gmail not receiving emails
- Email writing formal and informal
- Semi informal email
- Writing an email exercises
- Business email useful phrases
- Ess barracuda
- Most e-mail messages and memos
- How to start a formal email
- Email memo
- What is evault
- Memos and emails
- Accept your loneliness you are your only friend
- Goodbye to u my trusted friend
- Good morning good morning to you i am glad to see you
- Yesterday you met a friend of yours charlie
- We had misunderstanding
- Sometimes in life you find a special friend
- Potential energy of spring
- If you have problem with your friend
- You are pushing a friend on a sled
- Effective refusal skills
- Your friend forget to bring his money
- What makes you a good friend
- Imagine that you are preparing a project with your friend
- Good morning campers today's challenge is simple