1. Class Greeting

2. Chapter 7 Rational Expressions and Equations
Lesson 7-1b
Simplifying Rational Expressions

3. Objective: Students will solve real world word problems involving simplifying rational expressions.

4. Average Cost
A manufacturer has a setup cost of $6000 for the production of a new tennis racquet. The cost of labor and materials for producing each unit is $15.50.
(a) Write a rational expression that models the average cost per unit when x units are produced.
𝑥 𝑥
x ≠0
(b) Find the domain of the expression in part (a).
The domain is the set of natural numbers.
(c) Find the average cost per unit when 300 units are produced.
(300) 300 =
= 10,
= 35.50
Answer: The average cost per unit when 300 units are produced is $35.50.

5. Average Cost
A manufacturer has a setup cost of $4000 for the production of a new tennis racquet. The cost of labor and materials for producing each unit is $12.50.
(a) Write a rational expression that models the average cost per unit when x units are produced.
𝑥 𝑥
x ≠0
(b) Find the domain of the expression in part (a).
The domain is the set of natural numbers.
(c) Find the average cost per unit when 200 units are produced.
(200) 200 = =
= 32.50
Answer: The average cost per unit when 300 units are produced is $32.50.

6. Probability
The probability of hitting the shaded portion of the region with a dart is equal to the ratio of the shaded area to the total area of the figure. Find the probability.
𝑥(𝑥−3) 𝑥(𝑥+5)
= 𝑥 𝑥−3 𝑥(𝑥+5)
= 𝑥−3 𝑥+5
x ≠−5, 0
The excluded value appears
to be 0 but we must think a
about the problem more.
We know rectangles cannot have lengths and widths that are negative.
Since the sides are x, x, x – 3, and x + 5, x must be greater than 3.
𝑥−3 𝑥+5
Answer: the probability of hitting the shaded portion is
, x >3.

7. Probability
The probability of hitting the shaded portion of the region with a dart is equal to the ratio of the shaded area to the total area of the figure. Find the probability.
𝑥(𝑥−7) 𝑥(𝑥+2)
= 𝑥 𝑥−7 𝑥(𝑥+2)
= 𝑥−7 𝑥+2
𝑥−7
x ≠−2, 0
The excluded value appears
to be 0 but we must think a
about the problem more.
𝑥+ 2
We know rectangles cannot have lengths and widths that are negative.
Since the sides are x, x, x – 7, and x + 2, x must be greater than 7.
𝑥−7 𝑥+2
, x >7.
Answer: the probability of hitting the shaded portion is

8. Depreciation 𝑉= 2,000,000𝑡 36𝑡 + 14𝑡 2 2,000,000𝑡 36𝑡 + 14𝑡 2
The value V of an automobile t years after it is purchased is given by
𝑉= 2,000,000𝑡 36𝑡 + 14𝑡 2
(a) Simplify the rational expression. 1
Answer: 1,000, 𝑡
2,000,000𝑡 36𝑡 + 14𝑡 2
= 2,000,000𝑡 2𝑡(18 +7𝑡)
, t ≠0
(b) Use the model to estimate to estimate the value of the automobile
3 years after it is purchased.
1,000, (3)
= 1,000,
= 1,000,000 39
= 25,
Answer: The value of an automobile is $25,641.03
3 years after it is purchased.

9. Depreciation 𝑉= 2,500,000𝑡 30𝑡 + 35𝑡 2 500,000 6 +7(3) = 500,000 6 +21
The value V of an automobile t years after it is purchased is given by
𝑉= 2,500,000𝑡 30𝑡 + 35𝑡 2
(a) Simplify the rational expression.
Answer: 500, 𝑡
t ≠0
(b) Use the model to estimate to estimate the value of the automobile
3 years after it is purchased.
500, (3)
= 500,
= 500,000 27
= 18,
Answer: The value of an automobile is $18,518.52
3 years after it is purchased.

10. Lesson Summary: Objective: Students will solve real world word problems involving simplifying rational expressions.

11. Preview of the Next Lesson: Objective: Students will learn how to multiply rational expressions.

12. Stand Up Please