1. Review 5.1 to 5.3
Practice for Quiz

2. Lesson Quiz: Part I Variation
1. The volume V of a pyramid varies jointly as the area of the base B and the height h, and V = 24 ft3 when B = 12 ft2 and h = 6 ft. Find B when V = 54 ft3 and h = 9 ft.
18 ft2
2. The cost per person c of chartering a tour bus varies inversely as the number of passengers n. If it costs $22.50 per person to charter a bus for 20 passengers, how much will it cost per person to charter a bus for 36 passengers?
$12.50

3. Example 3
Given: y varies inversely as x, and y = 4 when x = 10. Write and graph the inverse variation function. k x
y =
y varies inversely as x. k 10
Substitute 4 for y and 10 for x.
4 =
k = 40
Solve for k. 40 x
Write the variation formula.
y =

4. Example 3 Continued
To graph, make a table of values for both positive and negative values of x. Plot the points, and connect them with two smooth curves. Because division by 0 is undefined, the function is undefined when x = 0. x y –2
–20 –4
–10 –6
–20/3 –8 –5 x y 2 20 4 10 6
20/3 8 5

5. 5.2 Simplifying Rational Expressions Example 1
Simplify. Identify any x-values for which the expression is undefined.
6x2 + 7x + 2
6x2 – 5x – 5
(2x + 1)(3x + 2)
(3x + 2)(2x – 3)
(2x + 1)
(2x – 3)
Factor; then divide out common factors. =
The expression is undefined at ????

6. Example 2: Multiplying Rational Expressions
Multiply. Assume that all expressions are defined.
3x5y3
2x3y7 
10x3y4
9x2y5
x – 3
4x + 20 
x + 5
x2 – 9 A. B.
3x5y3
2x3y7 
10x3y4
9x2y5 3 5
x – 3
4(x + 5) 
x + 5
(x – 3)(x + 3) 3
5x3
3y5 1
4(x + 3)

7. Dividing: Example
Divide. Assume that all expressions are defined.
2x2 – 7x – 4
x2 – 9 ÷
4x2– 1
8x2 – 28x +12
2x2 – 7x – 4
x2 – 9 
8x2 – 28x +12
4x2– 1
(2x + 1)(x – 4)
(x + 3)(x – 3) 
4(2x2 – 7x + 3)
(2x + 1)(2x – 1)
(2x + 1)(x – 4)
(x + 3)(x – 3) 
4(2x – 1)(x – 3)
(2x + 1)(2x – 1)
4(x – 4)
(x +3)

8. Example 5: Solving Simple Rational Equations
Solve. Check your solution.
x2 – 3x – 10
x – 2
= 7
(x + 5)(x – 2)
(x – 2)
= 7
Note that x ≠ 2.
x + 5 = 7
x = 2
Because the left side of the original equation is undefined when x = 2, there is no solution.