Rational Expressions Chapter 8-4, page 527 St. Augustine Preparatory School November 2, 2015.
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Transcript of Rational Expressions Chapter 8-4, page 527 St. Augustine Preparatory School November 2, 2015.
![Page 1: Rational Expressions Chapter 8-4, page 527 St. Augustine Preparatory School November 2, 2015.](https://reader036.fdocuments.net/reader036/viewer/2022081603/5697c0141a28abf838ccd274/html5/thumbnails/1.jpg)
Rational ExpressionsChapter 8-4, page 527
St. Augustine Preparatory SchoolNovember 2, 2015
![Page 2: Rational Expressions Chapter 8-4, page 527 St. Augustine Preparatory School November 2, 2015.](https://reader036.fdocuments.net/reader036/viewer/2022081603/5697c0141a28abf838ccd274/html5/thumbnails/2.jpg)
Quiz
Wednesday- All multiple choice- Quiz will be on your device as usual, so make
sure it is charged- Everything from the in class, translations, and
todays class will be on the quiz - Tomorrow’s class will not be on the quiz
![Page 3: Rational Expressions Chapter 8-4, page 527 St. Augustine Preparatory School November 2, 2015.](https://reader036.fdocuments.net/reader036/viewer/2022081603/5697c0141a28abf838ccd274/html5/thumbnails/3.jpg)
Rational Expressions
• A rational expression is the quotient of two polynomials
and are both rational expressions and are equivalent to each other
![Page 4: Rational Expressions Chapter 8-4, page 527 St. Augustine Preparatory School November 2, 2015.](https://reader036.fdocuments.net/reader036/viewer/2022081603/5697c0141a28abf838ccd274/html5/thumbnails/4.jpg)
Simplest Form
• A rational expression is in simplest form when its numerator and denominator are polynomials that have no common divisors
![Page 5: Rational Expressions Chapter 8-4, page 527 St. Augustine Preparatory School November 2, 2015.](https://reader036.fdocuments.net/reader036/viewer/2022081603/5697c0141a28abf838ccd274/html5/thumbnails/5.jpg)
Simplifying Rational Expressions
• When simplifying a rational expression, both the numerator and the denominator are divided by the same divisor
• Restrictions must used for any value of x that will make the expression 0– Some restrictions will appear or disappear as you
simplify the expression, however, they must be included (you will see an example of this next slide)
![Page 6: Rational Expressions Chapter 8-4, page 527 St. Augustine Preparatory School November 2, 2015.](https://reader036.fdocuments.net/reader036/viewer/2022081603/5697c0141a28abf838ccd274/html5/thumbnails/6.jpg)
Simplifying a Rational Expression
Simplify the expression
Simplified form with restrictions for the domain of the expression
![Page 7: Rational Expressions Chapter 8-4, page 527 St. Augustine Preparatory School November 2, 2015.](https://reader036.fdocuments.net/reader036/viewer/2022081603/5697c0141a28abf838ccd274/html5/thumbnails/7.jpg)
Practice – Simplify the following
a. b.
![Page 8: Rational Expressions Chapter 8-4, page 527 St. Augustine Preparatory School November 2, 2015.](https://reader036.fdocuments.net/reader036/viewer/2022081603/5697c0141a28abf838ccd274/html5/thumbnails/8.jpg)
Answers
a. b.
![Page 9: Rational Expressions Chapter 8-4, page 527 St. Augustine Preparatory School November 2, 2015.](https://reader036.fdocuments.net/reader036/viewer/2022081603/5697c0141a28abf838ccd274/html5/thumbnails/9.jpg)
Multiplying Rational Functions
Example: Multiply the following. Give the answer in simplest form
• Not as terrible as it sounds/looks• Factor all expressions and look for any
possible areas that will cancel• Make the cancelations and leave the rest as
your answer. Don’t forget restrictions
![Page 10: Rational Expressions Chapter 8-4, page 527 St. Augustine Preparatory School November 2, 2015.](https://reader036.fdocuments.net/reader036/viewer/2022081603/5697c0141a28abf838ccd274/html5/thumbnails/10.jpg)
Example
![Page 11: Rational Expressions Chapter 8-4, page 527 St. Augustine Preparatory School November 2, 2015.](https://reader036.fdocuments.net/reader036/viewer/2022081603/5697c0141a28abf838ccd274/html5/thumbnails/11.jpg)
Dividing Rational Expressions
Dividing by a rational expression is the same as multiplying by the reciprocal of the same expression
- Simple Example:3 divided by 1/4 = 123 multiplied by 4 = 12
To divide rational expressions, simply take the reciprocal of the divisor and multiply
![Page 12: Rational Expressions Chapter 8-4, page 527 St. Augustine Preparatory School November 2, 2015.](https://reader036.fdocuments.net/reader036/viewer/2022081603/5697c0141a28abf838ccd274/html5/thumbnails/12.jpg)
Example – divide the following
Note: x cannot equal 1 comes from the original expression for the divisor, where the denominator is x2 – 1. If x = 1, then x2 – 1 = 0.
![Page 13: Rational Expressions Chapter 8-4, page 527 St. Augustine Preparatory School November 2, 2015.](https://reader036.fdocuments.net/reader036/viewer/2022081603/5697c0141a28abf838ccd274/html5/thumbnails/13.jpg)
Application
• The school is planning on building a pool for next year. For safety reasons, the pool is required to have a fence around it. The school wants to maximize the area of the pool for a given amount of fencing. Should the school build a circle or a square pool?
![Page 14: Rational Expressions Chapter 8-4, page 527 St. Augustine Preparatory School November 2, 2015.](https://reader036.fdocuments.net/reader036/viewer/2022081603/5697c0141a28abf838ccd274/html5/thumbnails/14.jpg)
Answer
A given amount of fencing refers to the perimeter of the pool. The school also wants to maximize the area of the pool within the given amount of fencing. The two options are a square pool and a circular pool. If we divide the area of the pool by the perimeter to obtain a ratio, we will be able to see whether a square or a circle will maximize the area.
SquareCircle
Area = s2 , where s is one side Area = πr2
Perimeter = 4sPerimeter = 2πr
![Page 15: Rational Expressions Chapter 8-4, page 527 St. Augustine Preparatory School November 2, 2015.](https://reader036.fdocuments.net/reader036/viewer/2022081603/5697c0141a28abf838ccd274/html5/thumbnails/15.jpg)
SquareCircle
Given that the perimeter is going to be the same whether the pool is a circle or a square, we can use P in the equation, as opposed to the actual formula for perimeter. This will provide us with an equation for the ratio of area to perimeter for both a circle and a square that we can relate to each other. Comparing our two equations, we can see that for any given perimeter, we will receive more area by using a circle.
![Page 16: Rational Expressions Chapter 8-4, page 527 St. Augustine Preparatory School November 2, 2015.](https://reader036.fdocuments.net/reader036/viewer/2022081603/5697c0141a28abf838ccd274/html5/thumbnails/16.jpg)
Questions to Complete
Page 531: 12, 17, 19, 23, 25, 36
Challenge problem: 37