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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
Example 3
Given: y varies inversely as x, and y = 4 when x = 10. Write and
graph the inverse variation function.
y=
4=
k
x
k
10
k = 40
y=
y varies inversely as x.
Substitute 4 for y and 10 for
x.
Solve for k.
40
x
Write the variation formula.
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
–2
–4
–6
–8
y
–20
–10
–20/3
–5
x
2
4
6
8
y
20
10
20/3
5
5.2 Simplifying Rational Expressions Example 1
Simplify. Identify any x-values for which the expression is undefined.
6x2 + 7 x + 2
6x2 – 5x – 5
(2x + 1)(3x + 2)
(3x + 2)(2x – 3)
=
(2x + 1)
(2x – 3)
The expression is undefined at ????
Factor; then divide out common
factors.
Example 2: Multiplying Rational Expressions
Multiply. Assume that all expressions are defined.
A.
3x5y3
2x3y7
3
5
3x y3
2x3y7
5 x3
3y5
10x3y4


9x2y5
10x3y4
5
3
9x2y5
B.
x–3
4x + 20
x–3
4(x + 5)
1
4(x + 3)

x+5
x2 – 9

x+5
(x – 3)(x + 3)
Dividing: Example
Divide. Assume that all expressions are defined.
2 x2 – 7x – 4
x2 –
9
2x2 – 7x – 4
x2
–9
(2x + 1)(x – 4)
(x + 3)(x – 3)
(2x + 1)(x – 4)
(x + 3)(x – 3)
4(x – 4)
(x +3)
4 x 2– 1
÷
8x2 – 28x +12
8x2 – 28x +12

4x2– 1
4(2x2 – 7x + 3)

(2x + 1)(2x – 1)

4(2x – 1)(x – 3)
(2x + 1)(2x – 1)
Example 5: Solving Simple Rational Equations
Solve. Check your solution.
x2 – 3x – 10
=7
x–2
(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.

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