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Unit: Rational relationships

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Possible mastery points

Simplifying rational expressions

Learn
Intro to rational expression simplification
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Intro to rational expressions
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Reducing rational expressions to lowest terms
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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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Simplifying rational expressions (old video)
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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!

Quiz 1

Level up on the above skills and collect up to 300 Mastery points

Multiplying & dividing rational expressions

Learn
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
(Opens a modal)
Dividing rational expressions
(Opens a modal)
Multiplying rational expressions: multiple variables
(Opens a modal)
Dividing rational expressions: unknown expression
(Opens a modal)
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!

Quiz 2

Level up on the above skills and collect up to 300 Mastery points

Adding & subtracting rational expressions

Learn
Adding & subtracting rational expressions: like denominators
(Opens a modal)
Intro to adding & subtracting rational expressions
(Opens a modal)
Intro to adding rational expressions with unlike denominators
(Opens a modal)
Adding rational expression: unlike denominators
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Subtracting rational expressions: unlike denominators
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Least common multiple
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Least common multiple: repeating factors
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Subtracting rational expressions: factored denominators
(Opens a modal)
Least common multiple of polynomials
(Opens a modal)
Adding & subtracting rational expressions (advanced)
(Opens a modal)
Subtracting rational expressions
(Opens a modal)
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!
Least common multipleGet 3 of 4 questions to level up!
Add & subtract rational expressions: factored denominatorsGet 3 of 4 questions to level up!
Add & subtract rational expressionsGet 3 of 4 questions to level up!

Nested fractions

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Nested fractions
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Practice
Nested fractionsGet 3 of 4 questions to level up!

Quiz 3

Level up on the above skills and collect up to 600 Mastery points

Solving rational equations

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Rational equations intro
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Equations with one rational expression (advanced)
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Equations with rational expressions
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Equations with rational expressions (example 2)
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Practice
Rational equations introGet 3 of 4 questions to level up!
Rational equations (advanced)Get 3 of 4 questions to level up!
Rational equationsGet 3 of 4 questions to level up!

Quiz 4

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Direct and inverse variation

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Intro to direct & inverse variation
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Recognizing direct & inverse variation
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Recognizing direct & inverse variation: table
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Inverse variation word problem: string vibration
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Practice
Recognize direct & inverse variationGet 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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Practice
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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Practice
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

Learn
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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Quiz 5

Level up on the above skills and collect up to 500 Mastery points
Up next for you:

Unit test

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About this unit

Rational expressions are like fractions, but instead of integers in the numerator and the denominator, you have variable expressions! Learn how to work with such expressions. Namely, simplify, add, subtract, multiply, and divide them (much like fractions!). Then, solve some equations with rational expressions in them, and analyze the behavior of rational functions.