§6.2, 6.3 Assignment
Notes
1. Exercises from 6.2, 6.3
2. Read §6.6.
3. Quiz #6: 6.1 - 6.3, Cumulative section
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§6.2 - Multiplying and Dividing Rational Expressions
Notes
Multiplication
To multiply rational expressions, multiply the numerators, multiply the
denominators, and write the product in a simplified form.
Reminders
I
Keep track of the original domain restrictions. These restrictions will
not change.
I
Any expression can be made into a fraction by writing it as a fraction
over 1.
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§6.2 - Multiplying and Dividing Rational Expressions
Notes
#1 Example 1. Multiply
4x 3 y −6x 2 y 2
·
3xy 4
10x 4
#2 Example 2. Multiply
x
x −4
·
5x 2 − 20x 2x 2 + x − 3
#3 Example 4. Mulitply
x − y x 2 − xy − 2y 2
·
y2 − x2
3x − 6y
Always write the domain restrictions!!
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M 1010 §6.2, 6.3
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§6.2 - Multiplying and Dividing Rational Expressions
Notes
Division
To divide rational expressions, invert the divisor and multiply.
Reminders
I
Keep track of the original domain restrictions. These restrictions will
not change.
I
Division problems may gain domain restrictions.
M 1010 §6.2, 6.3
(Math 1010)
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§6.2 - Multiplying and Dividing Rational Expressions
Notes
#1 Example 7. Divide the rational expressions.
2x
x 2 − 2x
÷
3x − 12 x 2 − 6x + 8
#2 Example 8. Divide the rational expressions.
x2 − y2
2x 2 − 3xy + y 2
÷
2x + 2y
6x + 2y
#3 Exercise # 69. The number of jobs J, and population P in millions
and in Florida each, for 2001 through 2006 is modeled by
−0.69t + 8.94
,
−0.092t + 1
P = 0.352t + 15.97,
J=
1≤t≤6
1≤t≤6
Find a model Y for the number of jobs per person during these years.
Always write the domain restrictions!!
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§6.2 - Summary
Notes
Multiplying Rational Expressions
Step
Skill Used
Factor Top and Bottom
Factoring
Implied Domain
Solve when denominators are zero
Multiply Top and Bottom Multiply fractions
Simplify
Cancel common factors
Result
Write the product with implied domain
Dividing Rational Expressions
Step
Skill Used
Factor Top and Bottom
Factoring
Implied Domain
Solve when denominators are zero
Invert Divisor
Reciprocate Divisor
Multiply Top and Bottom Multiply fractions
Implied Domain
Solve when denominators are zero
Simplify
Cancel common factors
Result
Write the product with implied domain
(Math 1010)
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§6.3 - Adding and Subtracting Rational Expressions
Notes
To add or subtract rational expressions with like denominators, add or
subtract the numerators. Simplify the result.
To add or subtract rational expressions with unlike denominators, first find
the lowest common denominator of the fraction.
Reminders
I
After adding or subtracting, check if the result can be simplified.
I
The least common multiple of polynomials is the simplest polynomial
that is a multiple of each of the original polynomials. It must contain
each different factors, with each factor raised to the highest power
amongst all polynomials.
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§6.3 - Adding and Subtracting Rational Expressions
Notes
Find the least common multiple of:
# 1 Example 4.
(a) 6x, 2x 2 , 9x 3
(b) x 2 − x, 2x − 2
(c) 3x 2 + 6x, x 2 + 4x + 4
# 2 Exercise #23
5x 2 , 20x 3
# 3 Exercise 28
6x 2 , 15x(x − 1)
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§6.3 - Adding and Subtracting Rational Expressions
Notes
Add or subtract.
# 1 Exercise 51
7 14
+
a a2
# 2 Example 6
3
5
−
x −3 x +2
# 3 Exercise 63
x
5
−
x +3 x −2
# 4 Example 8
x
1
−
x 2 − 5x + 6 x 2 − x − 2
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§6.3 - Summary
Notes
Adding and subtracting rational expressions
Step
Implied Domain
Like Denominators
Simplify
Result
Unlike Denominators
Rewrite Rational Expressions
Like Denominators
Simplify
Result
(Math 1010)
Skill Used
Solve when denominators are zero
Add or subtract numerators only
Factor
Write result with implied domain
Find least common multiple of denominators
Write fraction times 11
Add or subtract numberators only
Factor
Write result with implied domain
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Notes
Notes