Khan Academy on a Stick
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 rational expressions (when you have one algebraic expression divided by another)!
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Simplifying rational expressions introduction
Simplifying Rational Expressions
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Simplifying rational expressions 1
U11_L1_T1_we1 Simplifying Rational Expressions 1
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Simplifying rational expressions 2
U11_L1_T1_we2 Simplifying Rational Expressions 2
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Simplifying rational expressions 3
U11_L1_T1_we3 Simplifying Rational Expressions 3
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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.
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Adding and subtracting rational expressions 2
U11_L1_T3_we2 Adding and Subtracting Rational Expressions 2
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Subtracting rational expressions
Subtracting Rational Expressions
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Simplifying first for subtracting rational expressions
Simplifying First for Subtracting Rational Expressions
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Adding and subtracting rational expressions
Adding and Subtracting Rational Expressions
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Adding and subtracting rational expressions 3
U11_L1_T3_we3 Adding and Subtracting Rational Expressions 3
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Rationalizing denominators of expressions
Rationalizing Denominators of Expressions
Adding and subtracting rational expressions
Well, rational expressions are just algebraic expressions formed by dividing one expression by another. In this tutorial, we'll see that, even though they may look hairy, adding and subtracting rational expressions involves most of what we know about adding and subtracting numeric fractions.
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Horizontal and vertical asymptotes of function
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Matching rational functions to their graphs
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Another rational function graph example
Another Rational Function Graph Example
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Asymptotes of rational functions
Asymptotes of Rational Functions
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A third example of graphing a rational function
A Third Example of Graphing a Rational Function
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Finding horizontal and vertical asymptotes
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.
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Partial fraction expansion 1
Introduction to partial fraction expansion
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Partial fraction expansion 2
A more complex problem
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Partial fraction expansion 3
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 least-common multiple of the lower-degree ones). This tutorial lets us think about going the other way--start with a rational expression with a higher degree denominator and break it up as the sum of simpler rational expressions.
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Ex 1: Multi step equation
Turning a rational equation into a linear equation.
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Rational equations
Rational Equations
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Solving rational equations 1
Solving Rational Equations 1
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Solving rational equations 2
Solving Rational Equations 2
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Solving rational equations 3
Solving Rational Equations 3
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Applying rational equations 1
Applying Rational Equations 1
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Applying rational equations 2
Applying Rational Equations 2
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Applying rational equations 3
Applying Rational Equations 3
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Extraneous solutions to rational equations
Extraneous Solutions to Rational Equations
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Rational inequalities
Two ways to solve a rational inequality (or an inequality involving a fractional expression)
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Rational inequalities 2
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.
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Multiplying and simplifying rational expressions
Multiplying and Simplifying Rational Expressions
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Multiplying and dividing rational expressions 1
Multiplying and Dividing Rational Expressions 1
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Multiplying and dividing rational expressions 2
Multiplying and Dividing Rational Expressions 2
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Multiplying and dividing rational expressions 3
Multiplying and Dividing Rational Expressions 3
Multiplying and dividing rational expressions
Let's extend what we know about multiplying and dividing fractions to rational expressions. It may look complicated, but it really is about applying some core principles of what fractions represent.