2. What is the Lowest Common Denominator (LCD)? 5.3 – Addition & Subtraction of Rational Expressions

3. What is the Lowest Common Denominator (LCD)? 5.3 – Addition & Subtraction of Rational Expressions

4. What is the Lowest Common Denominator (LCD)? 5.3 – Addition & Subtraction of Rational Expressions

5. Examples (Like Denominators): 5.3 – Addition & Subtraction of Rational Expressions

6. Examples (Like Denominators): 5.3 – Addition & Subtraction of Rational Expressions

7. Examples (Like Denominators): 5.3 – Addition & Subtraction of Rational Expressions

8. Examples: 15 5.3 – Addition & Subtraction of Rational Expressions

9. Examples: 40x 2 5.3 – Addition & Subtraction of Rational Expressions

10. Examples: 5.3 – Addition & Subtraction of Rational Expressions

11. Examples: 5.3 – Addition & Subtraction of Rational Expressions

12. Examples: 5.3 – Addition & Subtraction of Rational Expressions

13. Examples: continued 5.3 – Addition & Subtraction of Rational Expressions

14. Examples: 5.3 – Addition & Subtraction of Rational Expressions

15. Examples: continued 5.3 – Addition & Subtraction of Rational Expressions

16. Defn: A rational expression whose numerator, denominator, or both contain one or more rational expressions. 5.4 – Complex Fractions Complex Fractions

17. LCD: 12, 8LCD: 2424 2 3 5.4 – Complex Fractions

18. LCD: y y–yy–y 5.4 – Complex Fractions

19. LCD: 6xy 6xy 5.4 – Complex Fractions

20. LCD: 63 Outers over Inners 5.4 – Complex Fractions

21. Outers over Inners 5.4 – Complex Fractions

23. 5.5 – Equations with Rational Expressions LCD: 20

24. LCD: 5.5 – Equations with Rational Expressions

25. LCD: 6x 5.5 – Equations with Rational Expressions

26. LCD: x+3 5.5 – Equations with Rational Expressions

27. LCD: 5.5 – Equations with Rational Expressions

28. LCD: abxSolve for a 5.5 – Equations with Rational Expressions

30. Problems about Numbers If one more than three times a number is divided by the number, the result is four thirds. Find the number. LCD = 3x 5.6 – Applications

31. Problems about Work Mike and Ryan work at a recycling plant. Ryan can sort a batch of recyclables in 2 hours and Mike can sort a batch in 3 hours. If they work together, how fast can they sort one batch? Time to sort one batch (hours) Fraction of the job completed in one hour Ryan Mike Together 2 3 x 5.6 – Applications

32. Problems about Work Time to sort one batch (hours) Fraction of the job completed in one hour Ryan Mike Together 2 3 x hrs. LCD = 6x 5.6 – Applications

33. James and Andy mow lawns. It takes James 2 hours to mow an acre while it takes Andy 8 hours. How long will it take them to mow one acre if they work together? Time to mow one acre (hours) Fraction of the job completed in one hour James Andy Together 2 8 x 5.6 – Applications

34. Time to mow one acre (hours) Fraction of the job completed in one hour James Andy Together 2 8 x LCD: hrs. 8x 5.6 – Applications

35. A sump pump can pump water out of a basement in twelve hours. If a second pump is added, the job would only take six and two-thirds hours. How long would it take the second pump to do the job alone? Time to pump one basement (hours) Fraction of the job completed in one hour 1 st pump 2 nd pump Together x 12 5.6 – Applications

36. Time to pump one basement (hours) Fraction of the job completed in one hour 1 st pump 2 nd pump Together x 12 5.6 – Applications

37. LCD: hrs. 60x 5.6 – Applications

38. Distance, Rate and Time Problems If you drive at a constant speed of 65 miles per hour and you travel for 2 hours, how far did you drive? 5.6 – Applications

39. A car travels six hundred miles in the same time a motorcycle travels four hundred and fifty miles. If the car’s speed is fifteen miles per hour faster than the motorcycle’s, find the speed of both vehicles. RateTimeDistance Motor- cycle Car x x + 15 450 mi 600 mi t t 5.6 – Applications

40. RateTimeDistance Motor- cycle Car x x + 15 450 mi 600 mi t t LCD: x(x + 15) 5.6 – Applications

41. x(x + 15) Motorcycle Car 5.6 – Applications

42. RateTimeDistance Up Stream Down Stream A boat can travel twenty-two miles upstream in the same amount of time it can travel forty-two miles downstream. The speed of the current is five miles per hour. What is the speed of the boat in still water? boat speed = x x - 5 x + 5 22 mi 42 mi t t 5.6 – Applications

43. RateTimeDistance Up Stream Down Stream boat speed = x x - 5 x + 5 22 mi 42 mi t t LCD:(x – 5)(x + 5) 5.6 – Applications

44. Boat Speed (x – 5)(x + 5) 5.6 – Applications

46. Dividing by a Monomial 5.7 – Division of Polynomials

47. Dividing by a Monomial 5.7 – Division of Polynomials

48. Review of Long Division 5.7 – Division of Polynomials

49. Long Division 5.7 – Division of Polynomials

50. Long Division 5.7 – Division of Polynomials

51. Long Division 5.7 – Division of Polynomials