R.6 Rational Expressions
Miller & Gerken, College Algebra 2e — Pages 68-81
Learning Objectives
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Identify domain restrictions for rational expressions
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Simplify rational expressions
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Multiply and divide rational expressions
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Add and subtract rational expressions
Key Concepts
Domain Restrictions
A rational expression \(\frac{p(x)}{q(x)}\) is undefined when \(q(x) = 0\).
Always find values that make the denominator zero and exclude them from the domain.
Operations with Rational Expressions
- Multiplication
\[\frac{a}{b} \cdot \frac{c}{d} = \frac{ac}{bd}\]
- Division
\[\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \cdot \frac{d}{c} = \frac{ad}{bc}\]
- Addition (same denominator)
\[\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}\]
- Addition (different denominators)
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Find the LCD, rewrite each fraction, then add numerators.
Examples
Example 1. Example 1 (p. XX)
Work through textbook example…
Practice Problems
Problem 1 (p. XX, #YY)
Problem:
My Work:
Answer:
Section Summary
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Key point 1
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Key point 2
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Key point 3