MTH 209 Week 3 - Biker John€¦ · MTH 209 Week 3 . Due for this week ... Complete the Week 3 study plan after submitting week 3 homework

MTH 209 Week 3

Due for this week…

Homework 3 (on MyMathLab – via the Materials

Link) The fifth night after class at 11:59pm.

Read Chapter 6.6, 8.4 and 11.1-11.5

Do the MyMathLab Self-Check for week 3.

Learning team hardest problem assignment.

Complete the Week 3 study plan after submitting

week 3 homework.

Participate in the Chat Discussions in the OLS

Slide 2 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Section 7.1

Introduction to

Rational

Expressions

Copyright © 2013, 2009, and 2005 Pearson Education, Inc.

Objectives

• Basic Concepts

• Simplifying Rational Expressions

• Applications

Basic Concepts

Rational expressions can be written as quotients

(fractions) of two polynomials.

Examples include:

2

3

2

, , 5

4

6

3

4 1

4 8

x x

x

x

xx

Example

If possible, evaluate each expression for the given

value of the variable.

a. b. c.

Solution

a. b. c.

1; 3

3x

x

2

; 43 4

ww

w

4; 5

4

ww

w

1; 3

3x

x

2

;3 4

4w

ww

4;

45

ww

w

1

3

1

3 6

2( )

3

4

( 44)

16

12 4

162

8

4 ( )

5)

5

( 4

91

9

Try Q 7,11,13,17 pg. 427

Example

Find all values of the variable for which each

expression is undefined.

a. b. c.

Solution

a. b. c.

2

1

x

2

4

w

w2

6

4w

2

1

x

2

4

w

w2

6

4w

Undefined

when x2 = 0 or

when x = 0.

Undefined

when w – 4 =

0 or when w =

4.

Undefined

when w2 – 4 =

0 or when w =

2.

Try Q 25,27,31,33 pg. 428

Example

Simplify each fraction by applying the basic principle

of fractions.

a. b. c.

Solution

a. The GCF of 9 and 15 is 3.

b. The GCF of 20 and 28 is 4.

c. The GCF of 45 and 135 is 45.

9

15

20

28

45

135

9

15 5

3

3

3

3

5

20

28 7

4

4

5

5

7

45

135

145

5 34

1

3

Try Q 39,43 pg. 428

Example

Simplify each expression.

a. b. c.

Solution

a. b. c.

2

16

4

y

y

3 12

4 16

x

x

2

2

25

2 7 15

x

x x

2

16

4

y

y

3 12

4 16

x

x

44

4

y

y y

4

y

3( )

4(

4

)4

x

x

3

4

2

2

25

2 7 15

x

x x

( )( 5)

(2

5

3)( )5

x

x

x

x

5

2 3

x

x

Example


a. b.

Solution

a. b.

7

2 14

y

y

8

8

x

x

7

2 14

y

y

1( )

2(

7

7)

y

y

1

2

8

8

x

x

(8 )

8

x

x

8

8

x

x

81

8

x

x

Try Q 51,55,61,79 pg. 428

Example

Suppose that n balls, numbered 1 to n, are placed in

a container and two balls have the winning number.

a. What is the probability of drawing the winning ball

at random?

b. Calculate this probability for n = 100, 1000 and

10,000.

c. What happens to the probability of drawing the

winning ball as the number of balls increases?

Solution

a. There are 2 chances of drawing the winning ball.

2

n

Try Q 105 pg. 429

Example (cont)

b. Calculate this probability for n = 100, 1000 and

10,000.

c. What happens to the probability of drawing the

winning ball as the number of balls increases?

The probability decreases.

2 1

100 50

2 1

1000 500

2 1

10,000 5000

Try Q 105 pg. 429

Section 7.2

Multiplication

and Division of

Rational

Expressions


Objectives

• Review of Multiplication and Division of Fractions

• Multiplication of Rational Expressions

• Division of Rational Expressions

Example

Multiply and simplify your answers to lowest terms.

a. b. c.

Solution

a.

b.

c.

4 5

9 7

415

5

2 5

7 8

4 5 20

9 7 63

4 15 4 6015 12

5 1 5 5

2 5 5 2 5 1 5

7 8 7 8 7 4 28

Try Q 5,7,9 pg. 435

Example

Divide and simplify your answers to lowest terms.

a. b. c.

Solution

a. b.

c.

1 3

6 5

618

7

4 11

5 15

1 3

6 5

618

7

4 11

5 15

1 5

6 3

5

18

1 6

7 18

6 1

7 18

1

21

60

55

4 15

5 11

12

11

12 5

11 5

Try Q 13,15,17 pg. 435

Example

Multiply and simplify to lowest terms. Leave your

answers in factored form.

a. b.

Solution

a. b.

2

6 5

10 12

x

x

3 4

2 1 3 9

x x

x x

2

6 5

10 12

x

x

210 12

6 5x

x

21

0

0

3

2

x

x

1

4x

3 4

2 1 3 9

x x

x x

( 3)( 4)

(2 1) 3 )9(x x

x x

( )( 4)

3(2 1)( 3)

3 x

x

x

x

4

3(2 1)

x

x

Example

Multiply and simplify to lowest terms. Leave your

answer in factored form.

Solution

2

2

16 3

9 4

x x

x x

2

2

( 3)

(

( )

4)

6

( 9)

1

x

x

x

x

2

2

16 3

9 4

x x

x x

( 3)( 4)( 4)

( 3)( 3 4))(x

xx x

x x

( 4)( )( )

( 3)

3

( 3 )

4

4)(

x

x

x x

x x

( 4)

( 3)

x

x

Try Q 29,31,41,45 pg. 435

Example

Divide and simplify to lowest terms.

a. b.

Solution

a. b.

3 2 1

6

x

x x

2

2

16 4

2 8 2

x x

x x x

3 2 1

6

x

x x

3 6

2 1

x

x x

18

(2 1)

x

x x

18

2 1x

2

2

16

2 8

4

2

x

x x

x

x

2

2

16

42 8

2x

x x

x

x

( 4)( 4) 2

( 2)( 4) 4

x x x

x x x

( )( )( )

( )( )(

4

2 4

24

)4

x

xx

x

x

x

1

Try Q 49,57,65 pg. 435

Section 7.3

Addition and

Subtraction

with Like

Denominators


Objectives

• Review of Addition and Subtraction of Fractions

• Rational Expressions Having Like Denominators

Example

Simplify each expression to lowest terms.

a. b.

Solution

a.

b.

4 1

7 7

1 5

9 9

4 1

7 7

4 1

7

5

7

1 5

9 9

1 5

9

6

9

2

3

Example

Simplify each expression to lowest terms.

a. b.

Solution

a.

b.

13 7

18 18

15 11

30 30

13 7

18 18

13 7

18

6

18

1

3

15 11

30 30

15 11

30

2

15

4

30

Try Q 7,9,11,13 pg. 442

To add two rational expressions having like

denominators, add their numerators. Keep

the same denominator.

C is nonzero

SUMS OF RATIONAL EXPRESSIONS

A B A B

C C C

Example

Add and simplify to lowest terms.

a. b.

Solution

a.

b.

4 1 2

3 3

x x

x x

2 2

5

7 10 7 10

x

x x x x

3

4

3

1 2

x x

x x

4 1 2

3

x x

x

3

5 1x

x

2 2

5

7 10 7 10

x

x x x x

2

5

7 10

x

x x

5

5 2

x

x x

1

2x

Try Q 19,25,33,35 pg. 442

Example

Add and simplify to lowest terms.

a. b.

Solution

a.

b.

7 4

ab ab

2 2 2 2

w y

w y w y

7 4

ab ab

7 4

ab

11

ab

2 2 2 2

w y

w y w y

2 2

w y

w y

( )( )

w y

w y w y

1

w y

Try Q 51,53,55 pg. 443

To subtract two rational expressions having

like denominators, subtract their numerators.

Keep the same denominator.

C is nonzero

DIFFERENCES OF RATIONAL EXPRESSIONS

A B A B

C C C

Example

Subtract and simplify to lowest terms.

a. b.

Solution

a.

b.

2 2

6 6x

x x

2 2

2 3 4

1 1

x x

x x

2 2

6 6x

x x

2

6 6x

x

2

6 6x

x

2

x

x

1

x

2 2

2 3 4

1 1

x x

x x

2

2 3 4

1

x x

x

1

1 1

x

x x

2

1

1

x

x

1

1x

Try Q 21,27,67 pg. 442-3

Example

Subtract and simplify to lowest terms.

Solution

7 2

2 2

a a

a a

7 2

2 2

a a

a a

7 ( 2)

2

a a

a

6 2

2

a

a

Try Q 31,59 pg. 442-3

Section 7.4

Addition and

Subtraction

with Unlike

Denominators


Objectives

• Finding Least Common Multiples

• Review of Fractions Having Unlike Denominators

• Rational Expressions Having Unlike Denominators

The least common multiple (LCM) of two or

more polynomials can be found as follows.

Step 1: Factor each polynomial completely.

Step 2: List each factor the greatest number

of times that it occurs in either

factorization.

Step 3: Find the product of this list of factors.

The result is the LCM.

FINDING THE LEAST COMMON MULTIPLE

Example

Find the least common multiple of each pair of

expressions.

a. 6x, 9x4 b. x2 + 7x + 12, x2 + 8x + 16

Solution


6x = 3 ∙ 2 ∙ x 9x4 = 3 ∙ 3 ∙ x ∙ x ∙ x ∙ x

Step 2: List each factor the greatest number of

times.

3 ∙ 3 ∙ 2 ∙ x ∙ x ∙ x ∙ x

Step 3: The LCM is 18x4.

Example (cont)

b. x2 + 7x + 12, x2 + 8x + 16


x2 + 7x + 12 = (x + 3)(x + 4)

x2 + 8x + 16 = (x+ 4)(x + 4)

Step 2: List each factor the greatest number of times.

(x + 3), (x + 4), and (x + 4)

Step 3: The LCM is (x + 3)(x + 4)2.

Try Q 15,19,27,29 pg. 451

Example


a. b.

Solution

a. The LCD is the LCM, 42.

b. The LCD is 60.

4 1

7 6

5 11

12 30

4 1

7 6

4 6 1 7

7 6 6 7

24 7

42 42

31

42

5 11

12 30

5 5 11 2

12 5 30 2

25 22

60 60

3

60

1

20

Try Q 45,47 pg. 452

Example

Find each sum and leave your answer in factored

form.

a. b.

Solution

a. The LCD is x2.

b.

2

2 5

x x

4 3

1 1x x

2

2 5

x x

2

2 5x

x x x

2 2

2 5x

x x

2

2 5x

x

4 3

1 1x x

4 3 1

1 1 1x x

4 3

1 1x x

1

1x

Try Q 53,65,71 pg. 452

Example

Simply the expression. Write your answer in lowest

terms and leave it in factored form.

Solution

The LCD is x(x + 7).

3 5

7

x

x x

3 5

7

x

x x

3 7 5

7 7

x x x

x x x x

3 7 5

7 7

x x x

x x x x

3 7 5

7

x x x

x x

2 4 21 5

7

x x x

x x

2 21

7

x x

x x

Example

Simplify the expression. Write your answer in lowest

terms and leave it in factored form.

Solution

2 2

6 5

6 9 9x x x

6 5

3 3 3 3x x x x

2 2

6 5

6 9 9x x x

6 5

3 3 3 33

33

3

x

x x xx x

x

x

6 3 5 3

3 3 3 3 3 3

x x

x x x x x x

6 18 5 15

3 3 3

x x

x x x

33

3 3 3

x

x x x

Try Q 63,77,79,81 pg. 452

Example

Add and then find the reciprocal of the result.

Solution

The LCD is RS.

1 1,

R S

1 1 1 1

R S R

R

S

S

S R

S R

RS RS

S R

RS

The reciprocal is

.RS

S R

Try Q 101 pg. 453

Section 7.6

Rational

Equations and

Formulas


Objectives

• Solving Rational Equations

• Rational Expressions and Equations

• Graphical and Numerical Solutions

• Solving a Formula for a Variable

• Applications

Rational Equations

If an equation contains one or more rational

expressions, it is called a rational equation.

Example

Solve each equation.

a. b.

Solution

a. b.

9 4

7 x

6

2 1x

x

9 4

7 x

9 28x

28

9x

6

2 1x

x

6

2 1 1

x

x

2 1 6(1)x x

22 6x x

22 6 0x x

2 3 2 0x x

2 3 0x

3

2x 2x

The solutions are 3

2 and .2

The solution is

28.

9

2 0x

Try Q 9,15,31,41 pg. 473

Example

Determine whether you are given an expression or

an equation. If it is an expression, simplify it and then

evaluate it for x = 4. If it is an equation, solve it.

a. b.

Solution

a. There is an equal sign, so it is an equation.

24

3 3

x x

x x

2 3 10

2 2

x x

x x

2

3 4 3 33 3

x xx x x

x x

2 4 12x x x

4x

3 12x The answer checks.

The solution is −4.

Example (cont)

b. There is no equals sign, so it is an expression.

The common denominator is x – 2, so we can add

the numerators.

2 3 10

2

x x

x

2 3 10

2 2

x x

x x

2 5

2

x x

x

5x

When x = 4, the expression evaluates 4 + 5 = 9.

2 3 10

2 2

x x

x x

Try Q 49,55 pg. 473

Example

Solve graphically and numerically.

Solution

Graph and

2

1x

x

1

2

1y

x

2 .y x

The solutions are −2 and 1.

x −3 −2 −1 0 1 2 3

−1 −2 −− 2 1 2

3

1

2(−2, −2)

(1, 1)

Example (cont)

Solve graphically and numerically.

Solution

Numerical Solution

2

1x

x

The solutions are −2 and 1.

x −3 −2 −1 0 1 2 3

−1 −2 −− 2 1

−3 −2 −1 0 1 2 3

1

2

1y

x

2

3

1

2

2y x

Try Q 75 pg. 474

Example

Solve the equation for the specified variable.

Solution

2 for C r r

2 for C r r

2

2 2

rC

2

Cr

Example


Solution

2 for

Ah A

B b

2h

b

A

B

( ) 2h B b A

( )

2

h B bA

Example


Solution

2 for S B sl s

2 for S B ls s

2 S B B B ls

2 S B ls

2

2 2

S B

l

sl

l

2

S Bs

l

Try Q 89,91,97 pg. 474

Example

A pump can fill a swimming pool ¾ full in 6 hours,

another can fill the pool ¾ full in 9 hours. How long

would it take the pumps to fill the pool ¾ full, working

together?

Solution

3

6 9 4

t t

336 36

6 9 4

t t

6 4 27t t

72

10t

The two pumps can fill the pool ¾ full in

hours.

72

10

Try Q 102 pg. 474

Section 7.7

Proportions

and Variation


Objectives

• Proportions

• Direct Variation

• Inverse Variation

• Analyzing Data

• Joint Variation

Proportions

A proportion is a statement (equation) that two

ratios (fractions) are equal.

The following property is a convenient way to solve

proportions:

a

b d

c is equivalent to ,ad bc

provided b ≠ 0 and d ≠ 0.

Example

On an elliptical machine, Francis can burn 370

calories in 25 minutes. If he increases his work time

to 30 minutes, how many calories will he burn?

Solution

Let x be the equivalent amount of calories.

25 30

370 x

Minutes Minutes=

Calories Calories

25 11,100x

444x Thus, in 30 minutes,

Francis will burn 444

calories.

Try Q 65 pg. 488

Example

A 6-foot tall person casts a shadow that is 8-foot

long. If a nearby tree casts a 32-foot long shadow,

estimate the height of the tree.

Solution

The triangles are similar because

the measures of its corresponding

angles are equal. Therefore corresponding sides are

proportional.

6 ft h

8 ft 32 ft

32

6 8

h

Height Shadow length=

Height Shadow length

8 192h

24h The tree is 24 feet tall.

Try Q 56 pg. 488

Example

Let y be directly proportional to x, or vary directly with

x. Suppose y = 9 when x = 6. Find y when x = 13.

Solution

Step 1 The general equation is y = kx.

Step 2 Substitute 9 for y and 6 for x in

y = kx. Solve for k.

Step 3 Replace k with 9/6 in the equation y = 9x/6.

Step 4 To find y, let x = 13.

9 6

9

6

y kx

k

k

9

6

9(13)

6

19.5

y x

y

y

Try Q 33 pg. 487

Example

The table lists the amount of pay for various hours

worked.

a. Find the constant of proportionality.

b. Predict the pay for 19 hours of work.

Hours Pay

6 $138

11 $253

15 $345

23 $529

31 $713

6, 138

11, 253

15, 345

23, 529

31, 713

0

100

200

300

400

500

600

700

800

0 10 20 30 40

Pa

y (

do

lla

rs)

Hours

Example (cont)

The slope of the line equals the proportionality, k. If

we use the first and last data points (6, 138) and (31,

713), the slope is

The amount of pay per hour is $23. The graph of the

line y = 23x, models the given graph.

To find the pay for 19 hours, substitute 19 for x.

713 138

31 6k

23

y = 23x,

y = 23(19)

y = 437

19 hours of work would

pay $437.00

Try Q 73 pg. 488

Example

Let y be inversely proportional to x, or vary inversely

with x. Suppose y = 6 when x = 4. Find y when x = 8.

Solution

Step 1 The general equation is y = k/x.

Step 2 Substitute 6 for y and 4 for x in

Solve for k.

Step 3 Replace k with 24 in the equation y = k/x.

Step 4 To find y, let x = 8.

64

24

ky

x

k

k

24

8

3

ky

x

y

y

Try Q 39 pg. 487

Example

Determine whether the data in each table represent

direct variation, inverse variation, or neither. For

direct and inverse variation, find the equation.

a.

b.

c.

x 3 7 9 12

y 12 28 32 48

x 5 10 12 15

y 12 6 5 4

x 8 11 14 21

y 48 66 84 126

Neither the product xy nor the ratio y/x

are constant in the data in the table.

Therefore there is neither direct

variation nor indirect variation in this

table. As x increases, y decreases. Because

xy = 60 for each data point, the

equation

y = 60/x models the data. This

represents an inverse variation.

The equation y = 6x models the

data. The data represents direct

variation.

Try Q 51a,53a,55a pg. 487-488

, 0 and 1,xf x a a a

Let x, y, and z denote three quantities.

Then z varies jointly with x and y if

there is a nonzero number k such that

JOINT VARIATION

.z kxy

Example

The strength S of a rectangular beam varies jointly

as its width w and the square of its thickness t. If a

beam 5 inches wide and 2 inches thick supports 280

pounds, how much can a similar beam 4 inches wide

and 3 inches thick support?

Solution

The strength of the beam is

modeled by S = kwt2.

2280 5 2k

280

5 4k

14k

Try Q 83 pg. 488

Example (cont)

Thus S = 14wt2 models the strength of this type of

beam. When w = 4 and t = 3, the beam can support

S = 14 ∙ 4 ∙ 32 = 504 pounds

Try Q 83 pg. 488

Section 10.1

Radical

Expressions

and Functions


Objectives

• Radical Notation

• The Square Root Function

• The Cube Root Function

Radical Notation

Every positive number a has two square roots, one

positive and one negative. Recall that the positive

square root is called the principal square root.

The symbol is called the radical sign.

The expression under the radical sign is called the

radicand, and an expression containing a radical

sign is called a radical expression.

Examples of radical expressions: 5

7, 6 2, and 3 4

xx

x

Example

Evaluate each square root.

a.

b.

c.

36

0.64

4

5

0.8

16

25

6

Try Q 15,17,19,21 pg. 641

Example

Approximate to the nearest thousandth.

Solution

38

6.164

Try Q 39 pg. 641

Example

Evaluate the cube root.

a.

b.

c.

3 64

3 125

1

2

5

31

8

4

Try Q 23,25,27,41 pg. 641

Example

Find each root, if possible.

a. b. c.

Solution

a.

b.

c.

4 256 5 243 4 1296

4 256

5 243

4 1296

4 because 4 4 4 4 256.

53 because ( 3) 243.

An even root of a negative number

is not a real number.

Try Q 33,35,37 pg. 641

Example

Write each expression in terms of an absolute value.

a. b. c.

Solution

a.

b.

c.

2( 5) 2( 3)x 2 6 9w w

2( 5)

2( 3)x

2 6 9w w

5 5

3x

2( 3)w 3w

Try Q 45,49,51 pg. 641

Example

If possible, evaluate f(1) and f(2) for each f(x).

a. b.

Solution

a. b.

( ) 5 1f x x 2( ) 4f x x

(1) 5(1) 1

6

f

( 2) 5( 2) 1

9 undefined

f

2(1) 1 4

5

f

2( 2) ( 2) 4

8

f

( ) 5 1f x x 2( ) 4f x x

Try Q 61,63 pg. 641

Example

Calculate the hang time for a ball that is kicked 75

feet into the air. Does the hang time double when a

ball is kicked twice as high? Use the formula

Solution

The hang time is

The hang time is

The hang times is less than double.

1( )

2T x x

1(75) 75

2T 4.3 sec

1(150) 150

2T 6.1 sec

Try Q 75,89 pg. 642

Example

Find the domain of each function. Write your answer

in interval notation.

a. b.

Solution

Solve 3 – 4x 0.

The domain is

( ) 3 4f x x 2( ) 4f x x

3 4 0

4 3

3

4

x

x

x

3, .4

b. Regardless of the value

of x; the expression is

always positive. The

function is defined for all

real numbers, and it

domain is , .

Try Q 75,89 pg. 641

Section 10.2

Rational

Exponents


Objectives

• Basic Concepts

• Properties of Rational Exponents

Example

Write each expression in radical notation. Then

evaluate the expression and round to the nearest

hundredth when appropriate.

a. b. c.

Solution

a. b.

c.

1/249 1/526 1/2

6x

1/249 49 7 1/526

1/2(6 )x 6x

Try Q 37,54,59,63 pg. 650

Example

Write each expression in radical notation. Evaluate

the expression by hand when possible.

a. b.

Solution

a.

b.

2/3

8 3/410

2/3

8 2

3 8 2

2 4

3/410 34 10 4 1000

Example

Write each expression in radical notation. Evaluate

the expression by hand when possible.

a. b.

Solution

a.

3/481 4/514

/4381

43/(81)

3

4 81

Take the fourth root of

81 and then cube it.

33

27

b. 4/514 Take the fifth root of 14

and then fourth it.

54/14

4

5 14

Cannot be evaluated

by hand.

Try Q 47,51 pg. 650

Example

Write each expression in radical notation and then

evaluate.

a. b.

Solution

a. b.

1/481 2/364

1/4812/364

1/4

1

81

4

1

81

1

3

3/2

1

64

2

3

1

64

2

1

4

1

16

Try Q 53,55 pg. 650

Example

Use rational exponents to write each radical

expression.

a.

b.

c.

d.

7 3x

3

1

b3/2 b

3/7 x

25 ( 1)x2/5( 1) x

2 24 a b2 2 1/4( ) a b

Try Q 53,55 pg. 650

Example

Write each expression using rational exponents and

simplify. Write the answer with a positive exponent.

Assume that all variables are positive numbers.

a. b. 4x x34 256x1/2 1/4x x

1/2 1/4x

3/4x

1/43(256 )x

1/4 3 1/4256 ( )x

3/44x

Example (cont)

Write each expression using rational exponents and

simplify. Write the answer with a positive exponent.

Assume that all variables are positive numbers.

c. d.

5

4

32x

x

1/33

27

x

1/5

1/4

(32 )x

x

1/5 1/5

1/4

32 x

x

1/5 1/42x

1/202x

1/20

2

x

1/3

3

27

x

1/3

3 1/3

27

( )x

3

x

Try Q 77,83,91,97 pg. 650

Example

Write each expression with positive rational

exponents and simplify, if possible.

a. b.

Solution

a.

b.

4 2x

1/4

1/5

y

x

1/4

1/2( 2)x

1/8( 2)x

1/5

1/4

x

y

4 2x

1/4

1/5

y

x

Try Q 85,89,95 pg. 650

Section 10.3

Simplifying

Radical

Expressions


Objectives

• Product Rule for Radical Expressions

• Quotient Rule for Radical Expressions

Product Rule for Radicals

Consider the following example:

Note: the product rule only works when the radicals

have the same index.

4 25 2 5 10

4 25 100 10

Example

Multiply each radical expression.

a.

b.

c.

36 4

3 38 27

4 41 1 1 1 1

4 16 4 256 4

3 38 27 216 6

4 441 1 1

4 16 4

36 4 144 12

Try Q 13,15,21 pg. 659

Example

Multiply each radical expression.

a.

b.

c.

2 4x x

3 23 5 10a a

44 4

3 7 2121

x y xy

y x xy

3 32 3 35 10 50 50a a a a

443 7x y

y x

2 4 6 3x x x x

Try Q 23,51,57,61 pg. 659-60

Example


a.

b.

c.

500

3 40

72

100 5 10 5

3 3 38 5 2 5

36 2 6 2

Try Q 73,75,77,79 pg. 660

Example

Simplify each expression. Assume that all variables

are positive.

a. b.

c.

449x575y

3 23 3 9a a w

4 249 7x x 4 325y y

4 325y y

25 3yy3 23 9a a w

3 327a w

3 33 27a w

33a w

Try Q 45,85,89,91 pg. 660

Example


a. b.

37 73 5a a1/2 1/37 7

1/3 1/5a 1/2 1/37 5/67 8/15a

1/3 1/5a a

Try Q 101,103,107 pg. 660

Quotient Rule

Consider the following examples of dividing radical

expressions:

4 2 2 2

9 3 3 3

4 4 2

9 39

Example

Simplify each radical expression. Assume that all

variables are positive.

a. b. 37

275

32

x3

3

7

27

3 7

3

5

5 32

x

5

2

x

Try Q 25,27,29 pg. 659

Example

Simplify each radical expression. Assume that all


a. b. 90

10

4x y

y

90

10

9

4x y

y

4x

32x

Try Q 33,39,41 pg. 659

Example

Simplify the radical expression. Assume that all


4

55

32x

y

5 4

55

32x

y

5 45

55

32 x

y

5 42 x

y

Try Q 95,97 pg. 660

Example

Simplify the expression.

Solution

1 1 x x

1 1 x x ( 1)( 1) x x

2 1 x

Example

Simplify the expression.

Solution

3 2

3

5 6

2

x x

x

3 2

3

5 6

2

x x

x3

( 3)( )

)2(

2

x

x

x

3 3 x

Try Q 63,67 pg. 660

End of week 3

You again have the answers to those problems not

assigned

Practice is SOOO important in this course.

Work as much as you can with MyMathLab, the

materials in the text, and on my Webpage.

Do everything you can scrape time up for, first the

hardest topics then the easiest.

You are building a skill like typing, skiing, playing a

game, solving puzzles.

Documents

MTH 209 Week 3 - Biker John€¦ · MTH 209 Week 3 . Due for this week ... Complete the Week 3 study plan after submitting week 3 homework