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Scientific Notation
Notation and Symbols
Linear Equations and Inequalities in One Variable
Graphing Equations in Three Variables
What the Standard Form of a Quadratic can tell you about the graph
Simplifying Radical Expressions Containing One Term
Adding and Subtracting Fractions
Multiplying Radical Expressions
Adding and Subtracting Fractions
Multiplying and Dividing With Square Roots
Graphing Linear Inequalities
Absolute Value Function
Real Numbers and the Real Line
Monomial Factors
Raising an Exponential Expression to a Power
Rational Exponents
Multiplying Two Fractions Whose Numerators Are Both 1
Multiplying Rational Expressions
Building Up the Denominator
Adding and Subtracting Decimals
Solving Quadratic Equations
Scientific Notation
Like Radical Terms
Graphing Parabolas
Subtracting Reverses
Solving Linear Equations
Dividing Rational Expressions
Complex Numbers
Solving Linear Inequalities
Working with Fractions
Graphing Linear Equations
Simplifying Expressions That Contain Negative Exponents
Rationalizing the Denominator
Decimals
Estimating Sums and Differences of Mixed Numbers
Algebraic Fractions
Simplifying Rational Expressions
Linear Equations
Dividing Complex Numbers
Simplifying Square Roots That Contain Variables
Simplifying Radicals Involving Variables
Compound Inequalities
Factoring Special Quadratic Polynomials
Simplifying Complex Fractions
Rules for Exponents
Finding Logarithms
Multiplying Polynomials
Using Coordinates to Find Slope
Variables and Expressions
Dividing Radicals
Using Proportions and Cross
Solving Equations with Radicals and Exponents
Natural Logs
The Addition Method
Equations
   
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Simplifying Rational Expressions

After studying this lesson, you will be able to:

  • Simplify rational expressions.

A rational expression is a fraction that contains at least one variable.

There are basically 2 steps to simplify a rational expression :

1. Factor the numerator and the denominator

2. Cancel

** Only a binomial can cancel a binomial.

** Never cancel part of a binomial or part of a trinomial. You can cancel part of a monomial.

 

I. Simplifying Monomials:

Example 1

 

This is actually a review. We already know how to simplify monomials.

First, cancel or reduce the coefficients. 10 and 8 reduces to 5 and 4

Second, divide the variables. Remember to subtract exponents when dividing.

This is the simplified expression.

 

Example 2

 

This is actually a review. We already know how to simplify monomials.

First, cancel or reduce the coefficients. 24 and 8 reduces to 3 and 1

Second, divide the variables. Remember to subtract exponents when dividing.

This is the simplified expression.

 

II. Dividing by a Monomial

Example 3

Divide each term in the numerator by 2x

 

This is the simplified expression.

 

Example 4

Divide each term in the numerator by 2x

 

This is the simplified expression.

 

Example 5

Divide each term in the numerator by 6

This is the simplified expression.

 

III. Dividing by a Binomial or Trinomial

 

Example 6

Factor the numerator and the denominator.

 

Cancel the binomials that are identical. (x+1) cancels (x+1)

 

Do not cancel the remaining x's... never cancel part of a binomial

 

Example 7

Factor the numerator and the denominator.

 

Factor Completely

 

Cancel the 3's and cancel (m+4)

 

Example 8

Factor the numerator and the denominator.

 

Factor out 2 in the numerator and -1 in the denominator

 

Factor Completely

 

Cancel out ( x - y )

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