Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
Intermediate Algebra
Factoring Rational Expressions Rational Equations and Applications Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
Precalculus I / College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Precalculus II / Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III

Course: Intermediate Algebra
Topic: Rational Expressions
Subtopic: Operations II - Multiply & Divide

Overview

When multiplying fractions in arithmetic you reduce each fraction, cross cancel to simplify, then multiply. Similarly when multiplying algebraic rational expressions, you factor every numerator and denominator completely, reduce each fractions, cross cancel like factors, then multiply. Dividing two rational expressions is similar except that you flip the second fraction to convert to multiplication first.

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 8.2.1 Multiply two or more rational expressions factoring, reducing, and cross cancelling to simplify as needed
• 8.2.2 Divide two rational expressions by "flip and multiply"

Terminology

Terms you should be able to define: reduce, cross-cancel, reciprocate (a.k.a. flip)

Text Notes

Pay special attention to the examples that contain "opposites". Watch your signs! There is lots of factoring throughout this section. Factor carefully!