Khan Academy on a Stick
Ratios and rational expressions
You have probably been wondering whether our powers of algebraic problem solving break down if we divide by the variable or we have entire expressions in denominator of a fraction. Well, they don't! In this topic, you'll learn how to interpret and manipulate algebraic ratios and rational expressions (when you have one algebraic expression divided by another)!

The Golden Ratio
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An introduction to one of the most amazing ideas/numbers in mathematics

Ratio problem with basic algebra (new HD)
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A slightly more involved ratio problem with algebra

Writing proportions
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Setting up proportions to solve a word problem

More advanced ratio problemwith Algebra (HD version)
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More advance ratio problem with algebra.

Advanced ratio problems
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More advanced ratio problems

Alternate Solution to Ratio Problem (HD Version)
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An alternate solution to the advanced ratio problem in the last video.

Another Take on the Rate Problem
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Another Take on the Rate Problem

Find an Unknown in a Proportion
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t2 Find an Unknown in a Proportion

Find an Unknown in a Proportion 2
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t2 Find an Unknown in a Proportion 2
 Proportions 2 exercise examples

Mountain height word problem
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Using some basic algebra to solve what looks like a hairy word problem that involves proportions.
Ratios with algebra
You remember a thing or two about ratios and proportions from you prealgebra days. Well, how can we use these same ideas to solve problems in algebra. This tutorial reintroduces ratios in an algebraic context and helps us solve some awesome problems!

Simplifying Rational Expressions Introduction
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Simplifying Rational Expressions

Simplifying Rational Expressions 1
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U11_L1_T1_we1 Simplifying Rational Expressions 1

Simplifying Rational Expressions 2
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U11_L1_T1_we2 Simplifying Rational Expressions 2

Simplifying Rational Expressions 3
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U11_L1_T1_we3 Simplifying Rational Expressions 3

Simplifying Rational Expressions Example 2
u15_L1_T1_we2 Simplifying Rational Expressions
Simplifying rational expressions
You get a rational expression when you divide one polynomial by another. If you have a good understanding of factoring quadratics, you'll be able to apply this skill here to help realize where a rational expression may not be defined and how we can go about simplifying it.

Adding and Subtracting Rational Expressions
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Adding and Subtracting Rational Expressions

Adding and Subtracting Rational Expressions 2
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U11_L1_T3_we2 Adding and Subtracting Rational Expressions 2

Adding and Subtracting Rational Expressions 3
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U11_L1_T3_we3 Adding and Subtracting Rational Expressions 3

Subtracting Rational Expressions
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Subtracting Rational Expressions

Simplifying First for Subtracting Rational Expressions
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Simplifying First for Subtracting Rational Expressions

Multiplying and Simplifying Rational Expressions
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Multiplying and Simplifying Rational Expressions

Multiplying and Dividing Rational Expressions 1
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Multiplying and Dividing Rational Expressions 1

Multiplying and Dividing Rational Expressions 2
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Multiplying and Dividing Rational Expressions 2

Multiplying and Dividing Rational Expressions 3
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Multiplying and Dividing Rational Expressions 3

Rationalizing Denominators of Expressions
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Rationalizing Denominators of Expressions
Rational expressions and equations
Have you ever wondered what would happen if you divide one polynomial by another? What if you set that equal to something else? Would it be as unbelievably epic as you suspect it would be? Well, rational expressions are just algebraic expressions formed by dividing one expression by another. We get a rational equation if we set that equal to something else. In this tutorial, we work through examples to understand and apply rational expressions and equations.

Asymptotes of Rational Functions
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Asymptotes of Rational Functions

Another Rational Function Graph Example
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Another Rational Function Graph Example

A Third Example of Graphing a Rational Function
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A Third Example of Graphing a Rational Function
Graphing rational functions
Rational functions are often not defined at certain points and have very interesting behavior has the input variable becomes very large in magnitude. This tutorial explores how to graph these functions, paying attention to these special features. We'll talk a lot about vertical and horizontal asymptotes.

Partial Fraction Expansion 1
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Introduction to partial fraction expansion

Partial Fraction Expansion 2
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A more complex problem

Partial Fraction Expansion 3
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Dealing with repeated factors
Partial fraction expansion
If you add several rational expressions with lower degree denominator, you are likely to get a sum with a higher degree denominator (which is the leastcommon multiple of the lowerdegree ones). This tutorial lets us think about going the other waystart with a rational expression with a higher degree denominator and break it up as the sum of simpler rational expressions.

Ex 1 Multi step equation
Turning a rational equation into a linear equation.

Rational Equations
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Rational Equations

Solving Rational Equations 1
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Solving Rational Equations 1

Solving Rational Equations 2
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Solving Rational Equations 2

Solving Rational Equations 3
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Solving Rational Equations 3

Applying Rational Equations 1
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Applying Rational Equations 1

Applying Rational Equations 2
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Applying Rational Equations 2

Applying Rational Equations 3
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Applying Rational Equations 3

Extraneous Solutions to Rational Equations
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Extraneous Solutions to Rational Equations

Rational Inequalities
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Two ways to solve a rational inequality (or an inequality involving a fractional expression)

Rational Inequalities 2
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Slightly harder rational inequality problem
Solving rational equations
The equations you are about to see are some of the hairiest in all of algebra. The key is to keep calm and don't let the rational equation be the boss of you.