Section 6.1 Rational Expressions. Finding undefined values. YouTube Video. The following are rational expressions. What can x not equal? 5 x.

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1 Section 6. Rational Epressions Finding undefined values. YouTube Video The following are rational epressions. What can not equal? 6 7 9

2 Finding The Domain of a Function YouTube Video Tr: 7 9

3 Monomials Rational Epressions Reducing YouTube Video 6 z 6 z z z Tr this one: c d c Trinomials X + X ) + + ) Tr this one: Tr this one: - 9

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5 Section 6. Adding/Subtracting Rational Epressions YouTube Video 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 ) ) p p ) ) t + 9t t+7 t 9 ) t t

7 Section 6. Comple Fractions YouTube Video ) 7 ) 7 ) a a ) ) 9 7)

8 Section 6. Solving Rational Equations. YouTube Video Rational Equations: ) Factor denominators m 9 m 6 Rational Equations: k k ) Factor denominators k m 9 m ) ) LCD m ) LCD k ) 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

10 Formulas with Rational Equations YouTube Video a, for c b c I ne, for r R nr v v ) t s, for t

11 6 9 m m ), 9 m m LCD ) 9 m m ) 9 ) 9 ) 9 ) 9 m m m m m ) 6 m m Eliminate LCD Simplifing comple fractions Rationals YouTube Video Solving Rational Equations Simplif rational fraction) epression 0) ) 0) ) ) ) 0) Add/Subtracting Rational Epressions ) ) ) ) ) ) ) ) ) 6 ) ) ) ) 6 6 LCD

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13 WORD PROBLEMS INVOLVING PROPORTIONS YouTube Video M shadow is feet long and I m 6 feet tall. How tall is a tree with a shadow of feet? We set = The height of the tree. Set up two ratios. One involving one comparison, and the other involving the variable. Like Ian s shadow to Ian s Height and The Trees shadow to the Trees Height. In this case the first sentence can be made into the first ratio and the unknown will be in the second ratio. tree me Ian' s Shadow Trees Shadow Ian' s Height Trees Height then solve to find the answer. 6 X feet feet 6 feet

14 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 bottles of ketchup to make gallons of sauce. How man bottles of ketchup are needed to make 0 gallons of sauce?. Jim can run miles in. hours. How man miles can he run in hours?. If three apples cost cents, how much would five apples cost?. To estimate the deer population of a forest preserve, wildlife biologists caught, tagged, and then released deer. A month later, the returned and caught a sample of 7 deer and found that of them were tagged. Based on this eperiment, how man deer lived in the forest preserve?

15 Rational Epressions - Uniform Motion Time) YouTube Video D R T T The president of a compan traveled 00 mi b jet and 00mi on a prop plane. The rate of the jet was four times the rate of the prop plane. The entire trip took hours. Distance Rate T Jet Prop Plane Time traveled b Jet= Time traveled b Prop Plane: Time traveled b Jet + Time traveled b Prop Plane = Total time traveled A engineer traveled 6 mi b car and then an additional 660 mi b plane. The rate of the plane was four times the rate of the car. The total trip took 6 hours. Find the rate of the car. Distance Rate T Time traveled b Car= Time traveled b Plane: Time traveled b Car + Time traveled b Plane = Total time traveled

16 . Mar drove from her apartment to her parent s house. She averaged 60 mph because traffic was light. On the return trip, which took. hrs. longer, she averaged onl mph on the same route. What is the distance between Mar s apartment and her parent s house? Distance Rate T. As part of a conditioning, a jogger ran mi in the same amount of time as it took a cclist to ride 0 mi. The rate of the cclist was mph faster than the rate of the jogger. Find the rate of the jogger and the rate of the cclist. Hint: the times are equal. Distance Rate T 6

17 Work Problems YouTube Video Rate= the speed at which a person/thing can perform, travel, or do something= Work completed Time to complete it. Eample: If Jimbo can mow one lawn in minutes. Then his rate would be: lawn minutes = lawns / minute Find the rate:. Johnn can wash 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. 7. Working together Jimm and Sall can mow lawn in t minutes. 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 = + 7

18 ) 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?. The time it takes Julia to rebuild a carb. is one hour more than the time it takes Julia s mom. If the work together the can rebuild a carb. in hr min. How long does it take Julia s mom to rebuild the carb.?