FACTOR KILL. + 6x. 3x 3 yz. Section 8.1, 8.2: Simplifying Rational Expressions and Multiplying Rational Expressions

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1 Section.,.: Simplifing Rational Epressions and Multipling Rational Epressions The following are rational epressions. What can not equal? 6 Monomials FACTOR KILL 6 z 6 z z z Tr this one: c d c Trinomials X + X + + ( + )( + 6) ( + ) Tr this one: Tr this one: - 9

3 Section.: LCD for Rational Epressions LCM Least Common Multiple LCM is the smallest multiple that two or more numbers share Find the LCM : each factor must be in the LCM and the largest eponent of each factor must be on that factor... Denominators: z, 9 z. Denominators: 6, z LCM: LCM:. Denominators:,. Denominators:, LCM: LCM:. Denominators:, LCM: 6. Denominators:, 6 LCM: 6. Denominators: 9, 9 LCM:

4 Find the LCM/LCD. 6ab, ab. 0,. 7, 7.,.,. 6 ; ; 7. ; ; 0

5 Section.: Adding/Subtracting Rational Epr. Rational Epressions: 9 ) Factor denominators ) LCD ) Multipl top and bottom ) Add or subtract ) Reduce if possible Rational Epressions: ) Factor denominators ) LCD ) Multipl top and bottom ) ( ) Add or subtract ) Reduce if possible

6 6 ) 6 ) ) ) t t ) 6) p p 7)

7 7 Section.: Comple Fractions. ) 7 ) 7 ) a a ) ) 9 6) 7)

8 Section.: Solving Rational Equations. Rational Equations: m 9 m 6 Rational Equations: k k k ) Factor denominators ) Factor denominators m 9 ( m ) ) LCD ) LCD ) Multipl both sides (all groupings) b the LCD ) Multipl both sides (all groupings) b the LCD m 9 ( m ). Solve the resulting equation. Solve the resulting equation

9 ) ) 6 7 w w w w a ) a a ) ) 6) 6 9

$Rationals 9 ( ), 9 ( )( ) ( )( ) GCF LCM/LCD Simplif rational (fraction) epression Simplifing comple fractions LCD 6 6 6$

10 Rationals 9 ( ), 9 ( )( ) ( )( ) GCF LCM/LCD Simplif rational (fraction) epression Simplifing comple fractions LCD Add/Subtracting Rational Epressions Solving Rational Equations Eliminate 9( m) m 9 m 6 m 9 ( m ) LCD 9( m ), m m 9( m) 9 6 ( m ) ( m ) m 9( m) 0

12 Section.7: Proportions and Work Problems X 6 Solve for : Set up a proportion and solve.. As part of a spring clearance, a men s store put dress shirts on sale, for $.9. How much will a business man pa if he bus five shirts?. A recipe for spaghetti sauce requires four 6-ounce bottles of ketchup to make gallons of sauce. How man bottles of ketchup are needed to make 0 gallons of sauce?. Francesca makes her own ricotta cheese for her restaurant. The ratio of buttermilk to whole milk in her recipe is to. How much of each tpe of milk will she need if she will use more cups of whole milk than buttermilk? Define our variable because we have an translation here. Amount of whole milk: Amount of buttermilk:

13 . If three apples cost cents, how much would five apples cost?. :9 = :?. Simplif the ratio :0. Sam is 6 ears old. His sister is ears old. What's the ratio of Sam's age to his sister's age? Give our answer in its simplest form.. A map scale is :0000. A distance on the map is measured to be.6cm. What's the actual distance in real life? Give our answer in metres. m 6. A recipe for vegetable curr needs 00 grams of rice, and it feeds people. How much rice would be needed for 7 people? g 7. $60 is to be divided between Brian and Kate in the ratio :. How much does Kate get? Questions -0 refer to a necklace like this which is being made using white and black beads, as shown:. What's the ratio of white beads to black beads, in its simplest form? 9. How man white beads would be needed to go with black beads? 0. The necklace uses 7 beads altogether. How man of these are black?. If a baboon gained pounds after eating 0 bananas, then how much would he gain after eating bananas?. In a gluten-free flour miture, the ratio of potato-starch flour to tapioca flour is to. If a miture contains more cups of potato-starch flour than tapioca flour, how much of each tpe of flour is in the miture?

14 Work Problems Work completed = Rate(time) W=R*T R= Rate= the speed at which a person/thing can perform, travel, or do something= Work completed Time to completeit. Eample: If Jimbo can mow one lawn in minutes. Then his rate would be: lawn minutes Find the rate:. Johnn can was 6 dogs in hours.. Tomm can write 0 words in minutes.. A clerk can stock a shelf in 0 minutes.. A clerk can stock a shelf in 0 minutes.. Sall can fill bottles ever t hours. 6. Jimm can squish ant ever t minutes. = lawns / minute 7. Working together Jimm and Sall can mow lawn in t minutes. Finding the work completed: Work completed = Rate(time). Johnn can wash 6 dogs in hours. How man dogs can he wash in hours?. Tomm can write 0 words in minutes. How man words can he write in minutes?. A clerk can stock a shelf in 0 minutes. How man shelves can he stock in minute?. A clerk can stock a shelf in 0 minutes. How man shelves can he stock in minute? So the work completed after one unit of time is the same as the rate itself. Wh?

15 E/ One grocer clerk can stock a shelf in 0 min. A second clerk requires 0 min to stock the same shelf. How long would it take to stock the shelf if the two clerks worked together? a) Clerk 's rate: Clerk 's rate: b) Rate together = Clerk 's rate + Clerk 's rate = + ) Jimm can mow a lawn in 7 minutes. Sall can mow a lawn in 0 minutes. How long would it take them to mow the lawn together? a) Jimm's rate: Sall's rate: b) Rate together = +. A small air conditioner can cool a room in 60 minutes. A larger air conditioner can cool the room in 0 minutes. How long would it take to cool the room with both air conditioners working together?. Jimm can stock three times as man shelves in the same time it takes Tomm to stock one shelf. If the work together, then it takes them two hours. How fast can Jimm stock one shelf and how fast can Tomm stock one shelf?

16 Section 9., 9.: Simplifing square roots Square roots want the root of the squares

17 Radical Land z t c 0 0 c 7

18 * Multiplication 7 Multipl: 7 How do ou multipl radicals? - Multipl the Radicals and simplif: Fractions a a 9a b 7a 6b 0

19 Section 9.: Adding and subtracting radicals Adding and Subtracting Radicals: + square root of threes + square root of threes = 7 square root of threes = b a b ab 6a 7b Section 9.: Combining Radicals Multipling Radicals review: 7 7 a a

20 Section 9.: Dividing Radicals a Check list: 6 b ) ) ) a 9 7a b 9 7a b Multipl: ).. Conjugate of is Conjugate of 7 is 7 What happens to the radicals when ou multipl an epression b its conjugate? 0

21 Rationalizing the Denominator: 7 z z 7 7 h

22 Section 9.6: Solving Radical Equations Warm up: ) ) ) 9 ) What does What does 7 Eplain. What do ou need to do to both sides of the equation to remove the Tr to solve the following and then check our answers:? ) 6) 7) Tr to finish the following: ) 9) Was problem or problem 9 faster? Which answer is void of radicals? Tr to Solve the following: 0) ) )

23 What must ou do before ou square both sides? True or false a) 6 Wh? b) 6 Wh? c) If =9, then Wh? ISOLATE the radical and square both sides 6 0 Check our answer Check our answers Check our answers Tr these: 0

24 Section 0.: Square root propert Square Root Propert. 9 = or = = or = = or = Solve: 7 Isolate the Square and then take the square root. 9 t 6 0 t z

25 Review: Solving using factoring 6 a Section 0.: Quadratic Formula a b c 0 b b ac a 0 Solve. k 6k

26 Solve. 0 0 Solve. 7 Solve for using completing the square: a b c 0 6

27 : Start with the radical 0,, 9 a ac b b Removing the, : false Check, : check Square root propert (one ) Completing the Square (two s)

Finding The Domain of a Function YouTube Video

Section. Rational Epressions Finding undefined values. YouTube Video The following are rational epressions. What can not equal? 7 9 Finding The Domain of a Function YouTube Video Tr: 7 9 Rational Epressions