1. Dear Power point User,
This power point will be best viewed as a slideshow. At the top
of the page click on slideshow, then click from the beginning.

2. Rational Expressions
Chapter 8

3. 8 Rational Expressions 8.1 Simplifying Rational Expressions
8.2 Multiplying and Dividing Rational Expressions
8.3 Finding the Least Common Denominator
8.4 Adding and Subtracting Rational Expressions
Putting It All Together
8.5 Simplifying Complex Fractions
8.6 Solving Rational Equations
8.7 Applications of Rational Equations

4. 8.7 Applications of Rational Equations
We have studied applications of linear and quadratic equations. Now we turn our
Attention to applications involving equations with rational expressions. We will
Continue you to use the five-step problem-solving method outlined in Section 3.2.
Solve Problems Involving Proportions
Example 1
The ratio of apple cider to ginger ale in a punch recipe is 3 to 4. Jill is making punch
for a wedding reception so that she will need 2 liters more of the ginger ale than the
apple cider. How much of each ingredient will she need?
Solution
Step 1: Read the problem carefully, and identify what we are being asked to find.
We must determine how much of each ingredient will be needed.
Step 2: Choose a variable to represent the unknown, and define the other
unknown in terms of this variable.
x = apple cider
x + 2= ginger ale
Continued on next slide…

5. Write a proportion. We will write our ratios in the form of
Step 3: Translate the information that appears in English into an algebraic equation.
Write a proportion. We will write our ratios in the form of
so that the numerators contain the same quantities and the denominators
contain the same quantities.
Number of liters of apple cider
Number of liters of ginger ale
The equation is
Step 4: Solve the equation.
Set the cross products equal.
Multiply.
Multiply.
Distribute.
Subtract 3x..
Step 4: Check the answer and interpret the solution as it relates to the problem.
Therefore, 6 liters of apple cider is needed and = 8 liters of ginger ale
is needed.

6. Solve Problems Involving Distance, Rate, and Time
In Section 3.6, we solved problems involving distance (d), rate (r), and time (t). The
Basic formula is d = rt. We can solve this formula for r and then for t to obtain
The problems in this section involve boats going with and against a current, and
planes going with and against the wind. Both situations use the same idea.
Suppose a boat’s speed is 18 mph in still water. If that same boat had a 4-mph
current pushing against it, how fast would it be traveling? (The current will cause
the boat to slow down.)
Boat traveling with the current
is said to be traveling downstream.
If the speed of the boat in still water is 18 mph and a 4-mph current is pushing the
Boat, how fast would the boat be traveling with the current? (The current will cause the boat to travel faster.)
Boat traveling against is said
to be traveling upstream.

7. We know that d = rt,so if we solve for t we get .
Example 2
A boat can travel 8 mi downstream in the same amount of time it can travel 6 mi
upstream. If the speed of the current is 2 mph, what is the speed of the boat in still
water?
Solution
Step 1: Read the problem carefully, and identify what we are being asked to find. First, we
must understand that “8 mi downstream” means 8 mi with the current, and “6 mi
upstream” means 6 miles against the current. We must find the speed of the boat in
still water.
Step 2: Choose a variable to represent the unknown, and define the other unknown in terms
of this variable.
x = the speed of the boat in still water
x+2 = the speed of the boat with the current (downstream)
x-2 = the speed of the boat against the current (upstream)
Step 3: Translate from English into an algebraic equation. Use a table to organize
the information.
We know that d = rt,so if we solve for t we get
Substitute information from tables to get
expression for time. d r t
Downstream
Upstream 8
x +2 6
x -2

8. Step 5: Check answer and interpret. Step 4: Solve the equation.
The problem states that it takes the boat the same amount of time to travel 8 mi
Downstream as it does to go 6 mi upstream. We can write an equation in English:
Time for boat to go 8 mi downstream = Times for boat to go 6 mi upstream.
Looking at the table we can write the algebraic equation using the expressions for
Time.
Step 5: Check answer and interpret.
Step 4: Solve the equation.
The speed of the boat in still water
Is 14 mph.
Check: The speed of the boat going
Downstream is = 16 mph, so
The time to travel downstream is
Multiply.
Multiply.
Set the cross
products equal.
Distribute.
Time to travel upstream is 14-2 =12.
Subtract 6x and add 16
Divide by 2.
Time Upstream = Time Downstream

9. Solve Problems Involving Work

10. Example 3
Write an equation and solve.
If Tara can paint the backyard fence in 3 hr but her sister, Grace, could paint the
Fence in 2 hr, how long would it take them to paint the fence together?
Solution