Chapter 9Chapter 9

Section 5Section 5

Adding and Subtracting Adding and Subtracting Rational ExpressionsRational Expressions

Review ProblemsReview Problems

Find the least common multiple of Find the least common multiple of the two numbers. the two numbers. 7, 217, 21 24, 1024, 10

11,1711,17

Add or SubtractAdd or Subtract

38

7

19

5 25

3

15

2

Add or SubtractAdd or Subtract

36

5

24

7 45

7

12

11

How to find the LCM/LCDHow to find the LCM/LCD(Least Common Multiple/Denominator)(Least Common Multiple/Denominator)

1.1. Factor the denominator into its Factor the denominator into its prime factors (as small as each will prime factors (as small as each will go).go).

2.2. Write each prime factor the Write each prime factor the greatest number of times it appears greatest number of times it appears in either expression.in either expression.

3.3. Simplify where possible.Simplify where possible.

Find the Least Common Find the Least Common MultipleMultiple

4x4x2 2 – 36 and 6x– 36 and 6x22 + 36x +54 + 36x +54

Find the Least Common Find the Least Common MultipleMultiple

3x3x2 2 – 9x – 30 and 6x + 30– 9x – 30 and 6x + 30

Find the Least Common Find the Least Common MultipleMultiple

5x5x2 2 + 15x + 10 and 2x + 15x + 10 and 2x22 – 8 – 8

Steps to Add/SubtractSteps to Add/Subtract

1.1. Factor the denominatorsFactor the denominators

2.2. Identify the LCD for multiplicationIdentify the LCD for multiplication

3.3. Multiply as neededMultiply as needed

4.4. Add/subtractAdd/subtract

5.5. SimplifySimplify

SimplifySimplify

33

5

45

12

x

x

xx

SimplifySimplify

84

3

124

12

x

x

xx

SimplifySimplify

153

4

1255

72

yy

y

SimplifySimplify

306

3

105363

22

x

x

xx

SimplifySimplify

633

12

693 22

xx

x

xx

x

HomeworkHomework

Re-teaching 9.5 AllRe-teaching 9.5 All

Day TwoDay Two

Complex FractionsComplex Fractions

A fraction that has a fraction in its A fraction that has a fraction in its numerator or denominator or bothnumerator or denominator or both

Ex:Ex:

Two methods to simplify:Two methods to simplify: 1. Multiply everything by the LCD1. Multiply everything by the LCD 2. Divide the numerator by the 2. Divide the numerator by the

denominatordenominator

11

13

12

x2-x

21

1

3

1

xx

x

yyx

Method 1: Multiplying by Method 1: Multiplying by LCDLCD

1.1. Find the LCD of Find the LCD of the ENTIRE the ENTIRE fractionfraction

2.2. Multiply Multiply everything by this everything by this LCD (notice that LCD (notice that the small the small fractions fractions disappear)disappear)

3.3. SimplifySimplify

45

31

y

x

xy

yx12

11

2. Dividing2. Dividing

1.1. Simplify the Simplify the numerator and numerator and denominatordenominator

2.2. Divide the Divide the numerator by the numerator by the denominatordenominator

45

31

y

x

y21

1

3

11

13

122

xx

xxx

HomeworkHomework

Practice 9.5Practice 9.5