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Finding the Greatest Common Factor
Factoring Trinomials
Absolute Value Function
A Summary of Factoring Polynomials
Solving Equations with One Radical Term
Adding Fractions
Subtracting Fractions
The FOIL Method
Graphing Compound Inequalities
Solving Absolute Value Inequalities
Adding and Subtracting Polynomials
Using Slope
Solving Quadratic Equations
Multiplication Properties of Exponents
Completing the Square
Solving Systems of Equations by using the Substitution Method
Combining Like Radical Terms
Elimination Using Multiplication
Solving Equations
Pythagoras' Theorem 1
Finding the Least Common Multiples
Multiplying and Dividing in Scientific Notation
Adding and Subtracting Fractions
Solving Quadratic Equations
Adding and Subtracting Fractions
Multiplication by 111
Adding Fractions
Multiplying and Dividing Rational Numbers
Multiplication by 50
Solving Linear Inequalities in One Variable
Simplifying Cube Roots That Contain Integers
Graphing Compound Inequalities
Simple Trinomials as Products of Binomials
Writing Linear Equations in Slope-Intercept Form
Solving Linear Equations
Lines and Equations
The Intercepts of a Parabola
Absolute Value Function
Solving Equations
Solving Compound Linear Inequalities
Complex Numbers
Factoring the Difference of Two Squares
Multiplying and Dividing Rational Expressions
Adding and Subtracting Radicals
Multiplying and Dividing Signed Numbers
Solving Systems of Equations
Factoring Out the Opposite of the GCF
Multiplying Special Polynomials
Properties of Exponents
Scientific Notation
Multiplying Rational Expressions
Adding and Subtracting Rational Expressions With Unlike Denominators
Multiplication by 25
Decimals to Fractions
Solving Quadratic Equations by Completing the Square
Quotient Rule for Exponents
Simplifying Square Roots
Multiplying and Dividing Rational Expressions
Independent, Inconsistent, and Dependent Systems of Equations
Graphing Lines in the Coordinate Plane
Graphing Functions
Powers of Ten
Zero Power Property of Exponents
The Vertex of a Parabola
Rationalizing the Denominator
Test for Factorability for Quadratic Trinomials
Trinomial Squares
Solving Two-Step Equations
Solving Linear Equations Containing Fractions
Multiplying by 125
Exponent Properties
Multiplying Fractions
Adding and Subtracting Rational Expressions With the Same Denominator
Quadratic Expressions - Completing Squares
Adding and Subtracting Mixed Numbers with Different Denominators
Solving a Formula for a Given Variable
Factoring Trinomials
Multiplying and Dividing Fractions
Multiplying and Dividing Complex Numbers in Polar Form
Power Equations and their Graphs
Solving Linear Systems of Equations by Substitution
Solving Polynomial Equations by Factoring
Laws of Exponents
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Systems of Linear Equations
Properties of Rational Exponents
Power of a Product and Power of a Quotient
Factoring Differences of Perfect Squares
Dividing Fractions
Factoring a Polynomial by Finding the GCF
Graphing Linear Equations
Steps in Factoring
Multiplication Property of Exponents
Solving Systems of Linear Equations in Three Variables
Solving Exponential Equations
Finding the GCF of a Set of Monomials
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Multiplying Rational Expressions

Objective Learn to multiply rational expressions.

In this lesson, you will learn to multiply rational expressions. The techniques are completely analogous to multiplying rational numbers (fractions). Keep this analogy in mind throughout the entire lesson.


Multiplying Rational Numbers

Remember that to multiply rational numbers, multiply the numerators and then divide by the product of the denominators. Then simplify by dividing by the common factors of the numerator and the denominator.


Example 1

Find .


The GCF of the numerator and the denominator is 6.
Cancel the GCF.

An alternative way to approach this problem is to divide by the common factors before multiplying.


Multiplying Rational Expressions

Multiplying rational expressions is done the same way. Multiply the numerators, and then divide the product by the product of the denominators. Then simplify by dividing the common factors of the numerator and the denominator.


Example 2

Find .


Method 1:

Cancel the GCF of the numerator and the denominator, 6yz.

Now just like with multiplying fractions, there is an alternative method. Namely, divide by the common factors before multiplying.

Method 2:

There are some problems that require factoring the polynomials in order to find the GCF of the numerator and denominator.


Example 3

Find .


To simplify, factor the quadratic expressions in the numerator and then cancel the common factors of the numerator and the denominator.

For practice, do one more example.


Example 4

Find .


First, find the common factors. To do this, factor the quadratic expression in the denominator.

Cancel the common factors.

We therefore conclude that

This technique is very important because it reinforces prior techniques like factoring and multiplication of rational numbers.

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