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2. Transparency 1a

3. LESSON 2 CONTENTS Example 1One Excluded Value Example 2Multiple Excluded Values Example 3Use Rational Expressions Example 4Expression Involving Monomials Example 5Expression Involving Polynomials Example 6Excluded Values

4. EXAMPLE 2-1A Exclude the values for which Subtract 7 from each side. Answer: b cannot equal –7. The denominator cannot equal zero. State the excluded value of

5. EXAMPLE 2-1B Answer: –3 State the excluded value of

6. EXAMPLE 2-2A Exclude the values for which The denominator cannot equal zero. Factor. Use the Zero Product Property to solve for a. or Answer: a cannot equal –3 or 4. State the excluded value of

7. EXAMPLE 2-2B Answer: 2, 3 State the excluded value of

8. EXAMPLE 2-3A The original mechanical advantage was 5. Landscaping Refer to Example 3 on page 649. Suppose Kenyi finds a rock that he cannot move with a 6-foot bar, so he gets an 8-foot bar. But this time, he places the fulcrum so that the effort arm is 6 feet long, and the resistance arm in 2 feet long. Explain whether he has more or less mechanical advantage with his new setup.

9. EXAMPLE 2-3B Simplify. Answer:Even though the bar is longer, because he moved the fulcrum he has a mechanical advantage of 3, so his mechanical advantage is less than before. Use the expression for mechanical advantage to write an expression for the mechanical advantage in the new situation.

10. EXAMPLE 2-3C Answer:Since the mechanical advantage is 3, Kenyi can lift 3 180 or 540 pounds with the longer bar. If Kenyi can apply a force of 180 pounds, what is the greatest weight he can lift with the longer bar?

11. EXAMPLE 2-3D Landscaping Sean and Travis are responsible for clearing an area for a garden. They come across a large rock that they cannot lift. Therefore, they use a 5-foot bar as a lever, and the fulcrum is 1 foot away from the rock. a. Use the formulato find the mechanical advantage. b. If they can apply a force of 200 pounds, what is the greatest weight they can lift? Answer: 4 Answer: 800 lb

12. EXAMPLE 2-4A The GCF of the numerator and denominator is Divide the numerator and denominator by 1 1 Simplify Answer: Simplify.

13. EXAMPLE 2-4B Simplify Answer:

14. EXAMPLE 2-5A Factor. Divide the numerator and denominator by the GCF, x – 7. 1 1 Simplify Answer: Simplify

15. EXAMPLE 2-5B Simplify Answer:

16. EXAMPLE 2-6A Divide the numerator and denominator by the 1 1 SimplifyState the excluded values of x. Factor. Simplify. Answer:

17. EXAMPLE 2-6B Exclude the values for whichequals 0. The denominator cannot equal zero. Factor. Zero Product Property

18. EXAMPLE 2-6C Evaluate. Simplify. Check Verify the excluded values by substituting them into the original expression.

19. EXAMPLE 2-6D Evaluate. Simplify. Answer:The expression is undefined when and Therefore,

20. EXAMPLE 2-6E Answer: SimplifyState the excluded values of w.

21. END OF LESSON 2