# Rationals

**4.1 Adding & Subtracting Rational Expressions - like & unlike denominators**

**Explanation**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)

**4.2 Adding & Subtracting Rational Expressions - finding the LCM**

**Explanation**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

**4.3 Simplifying Rational Expressions**

**Explanation:**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)

**4.4 Multiplying & Dividing Rational Expressions**

**Explanation:**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)

**4.5 Solving Rational Equations**

**Explanation:**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?

**4.6 Word Problems with Rational Equations**

**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

**4.7 Type of Numbers and Closure Property **

**Explanation**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)

**4.8 Honors: ****D****omain**** ****of ****R****ational ****F****unctions **

**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

**4.9 Honors: ****End behavior of Rational Functions**

**Explanation:**Khan video: End behavior of rational functions

**Practice:**Khan exercise: End behavior of rational functions

**4.10 Honors: Sketching a Rational Function**

**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**