1. Class Greeting

2. Chapter 7 Rational Expressions and Equations
Lesson 7-3b
Adding and Subtracting Rational Expressions

3. Objective: Students will solve real world word problems involving adding and subtracting rational expressions.

4. Boat Travel
A boater travels 8 miles upstream (against the current) and 8 miles downstream (with the current). The speed of the current is 2 miles per hour. An expression for the time (in hours) it takes the boater to travel upstream is
8 𝑟+2 .
An expression for the time (in hours) it takes the boater to travel downstream is
8 𝑟 −2 .
a. Write and an expression for the total travel time (in hours) of the boater.
8 𝑟 −2 + 8 𝑟+2
Answer:

5. b. Simplify.
8 𝑟 −2 + 8 𝑟+2
8(𝑟+2) (𝑟 −2)(𝑟+2) + 8(𝑟−2) (𝑟+2)(𝑟−2)
What is the domain of r?
It appears that r cannot
equal -2 and 2 but we must think about
what is happening in the problem and…
8𝑟+16 𝑟 2 −4 + 8𝑟−16 𝑟 2 −4
if r = 2 the boat doesn’t move and if r < 2
16𝑟 𝑟 2 −4
the boat goes backwards, so…
Answer: The total travel time of the boater is 16𝑟 𝑟 2 −4 hours
and r > 2.

6. Boat Travel
A boater travels 4 miles upstream (against the current) and 4 miles downstream (with the current). The speed of the current is 3 miles per hour. An expression for the time (in hours) it takes the boater to travel upstream is
4 𝑟+3 .
An expression for the time (in hours) it takes the boater to travel downstream is
4 𝑟 −3 .
a. Write and an expression for the total travel time (in hours) of the boater.
4 𝑟 −3 + 4 𝑟+3
Answer:

7. b. Simplify.
4 𝑟 −3 + 4 𝑟+3
4(𝑟+3) (𝑟 −3)(𝑟+3) + 4(𝑟−3) (𝑟+3)(𝑟−3)
What is the domain of r?
It appears that r cannot
equal -3 and 3 but we must think about
what is happening in the problem and…
4𝑟+12 𝑟 2 −9 + 4𝑟−12 𝑟 2 −9
if r = 3 the boat doesn’t move and if r < 3
8𝑟 𝑟 2 −9
the boat goes backwards, so…
Answer: The total travel time of the boater is 8𝑟 𝑟 2 −9 hours
and r > 3.

8. Write an expression for the perimeter of the rectangle.
Geometry
Write an expression for the perimeter of the rectangle.
6 𝑦−2 + 6 𝑦−2
3 𝑦
3 𝑦 + +
6𝑦 𝑦(𝑦−2) + 6𝑦 𝑦(𝑦−2)
3𝑦−6 𝑦(𝑦−2)
3𝑦−6 𝑦(𝑦−2)
= 18𝑦−12 𝑦(𝑦−2) + +
6(3𝑦−2) 𝑦(𝑦−2)
Answer:

9. Write an expression for the perimeter of the rectangle.
Geometry
Write an expression for the perimeter of the rectangle.
7 𝑦−5
4 𝑦
7 𝑦−5 + 7 𝑦−5
4 𝑦
4 𝑦 + +
7𝑦 𝑦(𝑦−5) + 7𝑦 𝑦(𝑦−5)
4𝑦−20 𝑦(𝑦−5)
4𝑦−20 𝑦(𝑦−5)
= 22𝑦−40 𝑦(𝑦−5) + +
2(11𝑦−20) 𝑦(𝑦−5)
Answer:

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

11. Preview of the Next Lesson: Objective: The students will complete a practice test over sections 7-1 to 7-3.

12. Stand Up Please