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Rational functions

Cancelling common factors

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Intro to rational expression simplification
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Intro to rational expressions
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Intro to simplifying rational expressions
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Simplifying rational expressions: common monomial factors
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Simplifying rational expressions: common binomial factors
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Simplifying rational expressions: opposite common binomial factors
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Simplifying rational expressions (advanced)
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Simplifying rational expressions: grouping
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Simplifying rational expressions: higher degree terms
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Simplifying rational expressions: two variables
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Practice
Simplify rational expressions: common monomial factorsGet 3 of 4 questions to level up!
Simplify rational expressions: common binomial factorsGet 3 of 4 questions to level up!
Simplify rational expressions (advanced)Get 3 of 4 questions to level up!

End behavior of rational functions

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End behavior of rational functions
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End behavior of rational functionsGet 3 of 4 questions to level up!

Discontinuities of rational functions

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Discontinuities of rational functions
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Analyzing vertical asymptotes of rational functions
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Rational function points of discontinuityGet 3 of 4 questions to level up!
Analyze vertical asymptotes of rational functionsGet 3 of 4 questions to level up!

Graphs of rational functions

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Graphing rational functions according to asymptotes
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Graphs of rational functions: y-intercept
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Graphs of rational functions: horizontal asymptote
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Graphs of rational functions: vertical asymptotes
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Graphs of rational functions: zeros
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Graphs of rational functions (old example)
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Graphing rational functions 1
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Graphing rational functions 2
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Graphing rational functions 3
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Graphing rational functions 4
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Practice
Graphs of rational functionsGet 3 of 4 questions to level up!

Modeling with rational functions

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Analyzing structure word problem: pet store (1 of 2)
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Analyzing structure word problem: pet store (2 of 2)
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Rational equations word problem: combined rates
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Rational equations word problem: combined rates (example 2)
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Rational equations word problem: eliminating solutions
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Reasoning about unknown variables
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Reasoning about unknown variables: divisibility
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Structure in rational expression
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Multiplying and dividing rational expressions

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Multiplying & dividing rational expressions: monomials
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Multiplying rational expressions
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Dividing rational expressions
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Multiplying rational expressions
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Dividing rational expressions
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Multiplying rational expressions: multiple variables
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Dividing rational expressions: unknown expression
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Practice
Multiply & divide rational expressions (basic)Get 3 of 4 questions to level up!
Multiply & divide rational expressionsGet 3 of 4 questions to level up!
Multiply & divide rational expressions (advanced)Get 3 of 4 questions to level up!

Adding and subtracting rational expressions intro

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Adding & subtracting rational expressions: like denominators
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Intro to adding & subtracting rational expressions
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Intro to adding rational expressions with unlike denominators
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Adding rational expression: unlike denominators
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Subtracting rational expressions: unlike denominators
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Practice
Add & subtract rational expressions: like denominatorsGet 3 of 4 questions to level up!
Add & subtract rational expressions: unlike denominatorsGet 3 of 4 questions to level up!

Adding and subtracting rational expressions (factored)

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Subtracting rational expressions: factored denominators
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Least common multiple of polynomials
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Adding & subtracting rational expressions (advanced)
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Practice
Add & subtract rational expressions: factored denominatorsGet 3 of 4 questions to level up!

Adding and subtracting rational expressions (not factored)

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Subtracting rational expressions
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Add & subtract rational expressionsGet 3 of 4 questions to level up!

About this unit

Just as the polynomials are analogous to the integers, rational functions are analogous to the rational numbers. We will learn more about this analogy as we rewrite various rational expressions, and also think about their graphical behavior.