Rationals

• Explanation

  • Notes | Annotated

  • Khan video: Adding & subtracting rational expressions: like denominators

  • Khan article: Intro to adding & subtracting rational expressions (like and unlike denominators)

  • Khan video: Adding rational expression: unlike denominators

  • Khan video: Subtracting rational expressions: unlike denominators

• Practice Problems

  • Khan exercise: Add fractions with common denominators

  • Khan exercise: Adding & subtracting rational expressions: like denominators

  • Khan exercise: Add & subtract rational expressions (basic)

  • Worksheet #1

• Explanation

  • Notes | Annotated

  • Khan video: Subtracting rational expressions: factored denominators

  • Khan video: Least common multiple of polynomials

  • Khan article: Adding & subtracting rational expressions

  • Khan video: Subtracting rational expressions

• Practice Problems

  • Khan exercise: Add fractions with unlike denominators

  • Khan exercise: Add & subtract rational expressions: factored denominators

  • Khan exercise: Add & subtract rational expressions

  • Worksheet #1

• Explanation:

  • Notes | Annotated

  • Khan vide: Reducing rational expressions to lowest terms

  • Khan article: Intro to rational expressions

  • Khan article: Reducing rational expressions to lowest terms

  • Khan video: Simplifying rational expressions: common monomial factors

  • Khan video: Simplifying rational expressions: common binomial factors

  • Khan video: Simplifying rational expressions: opposite common binomial factors (honors)

  • Khan article: Simplifying rational expressions (advanced)

  • Khan video: Simplifying rational expressions: grouping

  • Khan video: Simplifying rational expressions: higher degree terms

• Practice Problems

  • Khan exercise: Reduce rational expressions to lowest terms: Error analysis

  • Khan exercise: Reduce rational expressions to lowest terms

  • Khan exercise: Simplify rational expressions (advanced)

  • Worksheet #1

• Explanation:

  • Notes | Annotated

  • Khan video: Multiplying & dividing rational expressions: monomials

  • Khan article: Multiplying rational expressions

  • Khan article: Dividing rational expressions

  • Khan video: Multiplying rational expressions

  • Khan video: Dividing rational expressions

  • Khan video: Multiplying rational expressions: multiple variables

  • Khan video: Dividing rational expressions: unknown expression

Practice Problems

• Khan exercise: Multiply & divide rational expressions: Error analysis

• Khan exercise: Multiply & divide rational expressions

• Khan exercise: Multiply & divide rational expressions (advanced)

• • Worksheet #1

• Explanation:

  • Notes | Annotated

  • Khan video: Equations with rational expressions

  • Khan video: Equations with rational expressions (example 2)

• Practice Problems

  • Khan exercise: Rational equations intro

  • Khan exercise: Rational equations - extra credit?

  • Worksheet #1

Explanation:

• Notes | Annotated

• Khan video: Analyzing structure word problem: pet store (1 of 2)

• Khan video: Analyzing structure word problem: pet store (2 of 2)

• Khan video: Rational equations word problem: combined rates

• Khan video: Rational equations word problem: combined rates (example 2)

• Khan video: Rational equations word problem: eliminating solutions

Practice Problems

• Worksheet #1 | Answers

Explanation

• Notes | Answers | Annotated

• Khan video: Polynomial subtraction & set closure

• Khan video: Intro to rational & irrational numbers (5:53)

• Khan video: Classifying numbers: rational & irrational (2:17)

• Khan video: Worked example: rational vs. irrational expressions (2:35)

• Khan video: Worked example: rational vs. irrational expressions (unknowns) (6:25)

Practice Problems

• Khan exercise: Classify numbers: rational & irrational

• Khan exercise: Rational vs. irrational expressions (extra credit)

• Worksheet

• Explanation:

  • Khan video: Discontinuities of rational functions

  • Khan video: Analyzing vertical asymptotes of rational functions

• Practice:

  • Khan exercise: Rational functions: zeros, asymptotes, and undefined points

  • Khan exercise: Analyze vertical asymptotes of rational functions

• Explanation:

  • Khan video: End behavior of rational functions

• Practice:

  • Khan exercise: End behavior of rational functions

• Explanation:

  • Khan video: Graphing rational functions according to asymptotes

  • Khan video: Graphs of rational functions: y-intercept

  • Khan video: Graphs of rational functions: horizontal asymptote

  • Khan video: Graphs of rational functions: vertical asymptotes

  • Khan video: Graphs of rational functions: zeros

  • Khan video: Graphing rational functions 1

  • Khan video: Graphing rational functions 2

  • Khan video: Graphing rational functions 3

  • Khan video: Graphing rational functions 4

• Practice:

  • Khan exercise: Graphs of rational functions

Review WS#1