Rational ExpressionsChapter 8-4, page 527

St. Augustine Preparatory SchoolNovember 2, 2015

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

Rational Expressions

• A rational expression is the quotient of two polynomials

and are both rational expressions and are equivalent to each other

Simplest Form

• A rational expression is in simplest form when its numerator and denominator are polynomials that have no common divisors

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)

Simplifying a Rational Expression

Simplify the expression

Simplified form with restrictions for the domain of the expression

Practice – Simplify the following

a. b.

Answers

a. b.

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

Example

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

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.

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?

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

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.

Questions to Complete

Page 531: 12, 17, 19, 23, 25, 36

Challenge problem: 37