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Warm up!

Warm up!. 3/11/09. Solve for x:. Learning Goal 16: Solving Rational Equations. There are 2 ways to solve Rational Expressions: Using the Cross Products Property Multiplying by the LCD. Vocabulary…. Rational Expression - .

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Warm up!

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  1. Warm up! 3/11/09 Solve for x:

  2. Learning Goal 16: Solving Rational Equations • There are 2 ways to solve Rational Expressions: • Using the Cross Products Property • Multiplying by the LCD

  3. Vocabulary… Rational Expression - An expression that can be written as a ratio of 2 polynomials. The denominator cannot be zero! Rational Equation - An equation that contains rational expressions Cross Products Property - For two ratios, if , then ad = bc.

  4. Steps to Solving using Cross Products: 1. Set cross products equal to each other 2. Simplify... 3. Put in standard form... 4. Factor and solve... 5. Check your solutions!

  5. Use the Cross Products Property to solve for x: 1. Set cross products equal to each other... 2. Simplify... 3. Put this in standard form... 4. Factor and solve... x = –6, 5

  6. 5. Checking your solutions... Plug these solutions back into your original problem to see if they “work” x = –6, 5

  7. Use the Cross Products Property to solve for x: 1. Set cross products equal to each other... 2. Simplify... 3. Put this in standard form... 4. Factor and solve...

  8. Use the Cross Products Property to solve for x: 1. Set cross products equal to each other... 2. Simplify... 3. Put this in standard form... 4. Factor and solve... x = –9, 4

  9. Practice: 1. 3. 2. 4.

  10. There are 2 ways to solve Rational Expressions: • Using the Cross Products Property • Multiplying by the LCD DONE!

  11. Recall, when adding fractions you need to find a common denominator... Example: The Least Common Denominator (or LCD) is: 6

  12. When adding rational expressions, you need to find a common denominator as well! Example: The LCD is: 12x The LCD is: (x+1)(x-1)

  13. Steps to solving rational equation: If, single fraction on either side, cross multiply like we did last class! IF THERE ARE 2 OR MORE TERMS ON ONE SIDE OF THE EQUAL SIGN: • Factor all the denominators, if necessary. • Find the LCD (of ALL denominators!) • Multiply each fraction by LCD. • Simplify and solve for the variable.

  14. We can use the LCD to help us solve rational equations... What is the LCD? 6 Multiply both sides by the LCD Solving Rational Equations Distribute the 6

  15. What is the LCD? 12 Multiply both sides by the LCD Solving Rational Equations

  16. What is the LCD? 15 Multiply both sides by the LCD Solving Rational Equations

  17. What is the LCD? 2(x + 5) Multiply both sides by the LCD Solving Rational Equations

  18. Solving Rational Equations

  19. What is the LCD? 5(x + 10) Multiply both sides by the LCD Solving Rational Equations

  20. LCD? Solving Rational Equations

  21. Write this in factored form to find the LCD Let’s look at a more challenging equation... Solve What is the LCD? (x + 5)(x – 2) x = –4, 1

  22. Solve the following rational equations: 1. 2. 3.

  23. HoMiE-wOrKpg. 178 1 – 15 oddyou must show work Test is Next Class!

  24. Homework: pg. 163 # 1 – 15 odd pg. 178 # 1 – 9

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