section 9.2: multiplying and dividing rational expressions
TRANSCRIPT
Section 9.2: Multiplying and Dividing Rational
Expressions
9.2 Lecture Guide: Multiplying and Dividing Rational Expressions
Objective 1: Multiply and divide rational expressions.
Algebraically Verbally Algebraic Example
If A, B, C and D are real polynomials and and then
1. _______________ the numerators and the denominators. Then write the product as a single fraction, indicating the product of the numerators and the product of the denominators.
2. _______________ this fraction by dividing the numerator and the denominator by any common nonzero factors.
0B 0,D
.A C ACB D BD
2 5 44 12 2 10x x yxy xy x
Multiplying Rational Expressions
Algebraically Verbally Algebraic Example
If A, B, C and D are real polynomials and and then
1. Rewrite the division problem as the product of the dividend and the _______________ of the divisor.
2. Perform the multiplication using the rule for multiplying rational expressions.
0,B 0,D
Dividing Rational Expressions
20 53 27 4 36
a aa a
A C A DB D B C
ADBC
0C
Perform the indicated operations and reduce all results tolowest terms. Assume the variables are restricted to valuesthat prevent division by zero.
1. 22 2515 33
2. 27 916 32
Perform the indicated operations and reduce all results tolowest terms. Assume the variables are restricted to valuesthat prevent division by zero.
3.2 3
4
30 1421 25x yy x
Perform the indicated operations and reduce all results tolowest terms. Assume the variables are restricted to valuesthat prevent division by zero.
4.226 13
15 45a ab b
Perform the indicated operations and reduce all results tolowest terms. Assume the variables are restricted to valuesthat prevent division by zero.
5. 2
2 2
3 4 44 6
x x xx x x
Perform the indicated operations and reduce all results tolowest terms. Assume the variables are restricted to valuesthat prevent division by zero.
6.25 5 24
12 7 7x y xx y x
Perform the indicated operations and reduce all results tolowest terms. Assume the variables are restricted to valuesthat prevent division by zero.
7.2
2
35 73 24 56
x xx x x
Perform the indicated operations and reduce all results tolowest terms. Assume the variables are restricted to valuesthat prevent division by zero.
8.2
2
16 449 7
x xx x
Perform the indicated operations and reduce all results tolowest terms. Assume the variables are restricted to valuesthat prevent division by zero.
9. 2 3
2
4 16 642 6 12
x x xx x x
Perform the indicated operations and reduce all results tolowest terms. Assume the variables are restricted to valuesthat prevent division by zero.
10.2 2
2 2
6 8 30 2 17 213 13 56 24 4 60x x x xx x x x
Perform the indicated operations and reduce all results tolowest terms. Assume the variables are restricted to valuesthat prevent division by zero.
11.2 2 2
3 2 2
42 5 6 363 4 1 3 12
x x x x xx x x x x
Perform the indicated operations and reduce all results tolowest terms. Assume the variables are restricted to valuesthat prevent division by zero.
12.2 7 3 5
2 2 2 2
32 25 125 484 5
x y x y x yx y x y x xy y
Perform the indicated operations and reduce all results tolowest terms. Assume the variables are restricted to valuesthat prevent division by zero.
13.2 3 2
2 2
49 25 502 9 35 4 40 3 70x x xx x x x x
Perform the indicated operations and reduce all results tolowest terms. Assume the variables are restricted to valuesthat prevent division by zero.
Determine the unknown expression in each equation.
2
2
5 2 3?
2 3 2 3x x xx x x
14.
Determine the unknown expression in each equation.
15. 2
2
6 11 3 3 1?
6 13 5 3 1x x xx x x
16. The number of items that a factory can produce in t hours per day is The total cost of operating the factory for t hours is given by
25 5 .N t t t 300 300.C t t
.A t C t N t The average cost per item produced is given by Write a formula for the average cost per item.
(a)
(b)
2 6 10 14 18 22t
A t
Use this function to complete the following table.
16. The number of items that a factory can produce in t hours per day is The total cost of operating the factory for t hours is given by
25 5 .N t t t 300 300.C t t
Describe what happens to the average cost when thenumber of hours the factory operates is reduced to almost 1 hour.
(c)
Describe what happens to the average cost when the number of hours the factory operates is increased to almost 24 hours.
(d)