5 Minute Check on Chapter 2 Transparency 3

5 -Minute Check on Chapter 2 Transparency 3 -1 1. Evaluate 42 - |x - 7| if x = -3 2. Find 4. 1 (-0. 5) Simplify each expression 3. 8(-2 c + 5) + 9 c 4. (36 d – 18) / (-9) 5. A bag of lollipops has 10 red, 15 green, and 15 yellow lollipops. If one is chosen at random, what is the probability that it is not green? 6. Standardized Test Practice: A 8/4 < 4/8 B Which of the following is a true statement -4/8 < -8/4 C -4/8 > -8/4 Click the mouse button or press the Space Bar to display the answers. D -4/8 > 4/8

Lesson 12 -2 Rational Expressions

Click the mouse button or press the Space Bar to display the answers.

Objectives • Identify values excluded from the domain of a rational function • Simplify rational expressions

Vocabulary • rational expression – • excluded values –

Key Concept xxxxx

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

Example 2 State the excluded value of 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.

Example 3 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. The original mechanical advantage was 5.

Example 3 cont Use the expression for mechanical advantage to write an expression for the mechanical advantage in the new situation. 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. If Kenyi can apply a force of 180 pounds, what is the greatest weight he can lift with the longer bar? Answer: Since the mechanical advantage is 3, Kenyi can lift 3 • 180 or 540 pounds with the longer bar.

Example 4 Simplify The GCF of the numerator and denominator is 1 Divide the numerator and denominator by 1 Answer: Simplify.

Example 5 Simplify Factor. 1 1 Answer: Divide the numerator and denominator by the GCF, x – 7. Simplify

Example 6 Simplify State the excluded values of x. Factor. 1 1 Answer: Divide the numerator and denominator by the Simplify.

Example 6 cont Exclude the values for which equals 0. The denominator cannot equal zero. Factor. Zero Product Property Answer: The expression is undefined when Therefore, and

Summary & Homework • Summary: – Excluded values are values of a variable that result in a denominator of zero • Homework: – pg