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9.5

9.5. Addition, Subtraction, and Complex Fractions. Learning Targets. Students should be able to… Find the Least Common Denominator Add and Subtract Rational Expressions. Warm-up. 1. Homework Check.

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9.5

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  1. 9.5 Addition, Subtraction, and Complex Fractions

  2. Learning Targets • Students should be able to… • Find the Least Common Denominator • Add and Subtract Rational Expressions

  3. Warm-up 1

  4. Homework Check

  5. Adding and Subtracting Rational ExpressionsExamples: To add or subtract rational expressions, you need a common denominator! 1. Already a common Denominator – combine The numerators! 2. Simplify!

  6. How to get a common denominator • 1. Factor denominators where possible • 2. Find factors that the fractions have in common • 3. Find factors that the fractions do NOT have in common • 4. Multiply the common factors by the non-common factors. This is your LCD

  7. Practice finding LCD’s What’s in common x – 2 NOTHING x What’s NOT in common x + 7 x, x + 6 5, x2 LCD (x + 7)(x – 2) 5x3 x(x + 6)

  8. Now let’s make them have the same denominator What’s missing for each fraction? Multiply top and bottom by missing factor Add the tops

  9. What’s missing for each fraction? Multiply top and bottom by missing factor Add the tops

  10. Factor denominators to help you see an LCD 3. 4. LCD Is (x+3)2(x-3) so we multiply each term by what is missing! LCD Is 3x3(2x+1),So we multiply each term by what is missing! Combine the numerators Check to see If you can simplify

  11. Simplifying Complex Fractions. Complex fraction: a fraction that contains a fraction in its numerator or denominator. To simplify, we multiply the top and bottom by the common denominator of the fractions within!

  12. Multiply by LCD Of (x – 4)(x + 1) Multiply Simplify

  13. Try it!

  14. Adding Rational Models. Example: Josh drove 42 miles and then took the train. The entire trip was 172 miles. The average speed of the train was 35 mi/h faster than the average speed of the car. Let x equal the average speed of the car and y equal the total time traveled. Then is the time the car traveled and is the time the train traveled. What is the time Josh traveled in the car if his rate is 35 mi/h? What is his time on the train if his car rate is 35 mi/h? Write a model that shows the total time it takes for the trip. At a speed of 50 mi/h, how long does the trip take?

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