COMBINATION OF MULTIPLICATION AND DIVISION OF RATIONAL EXPRESSION

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## LEARNING CENTER VIDEOS

Mathmatics

(under construction)These videos are available for student viewing in the Learning Center. Although many students are assigned to watch these tapes by their instructors, any student may watch them for personal improvement.

### BASIC MATHEMATICS -

Operation on the Whole Numbers

Standard Notation.

Addition and Perimeter

Subtraction.

Rounding and Estimating; Order

Multiplication.

Division.

Solving Equations.

Applications and Problem Solving.

Exponential Notation and Order of Operations.

Fractional Notation: Multiplication and Division.

Factorizations.

Divisibility.

Fractions.

Multiplication and Applications.

Simplifying.

Multiplying, Simplifying, and Applications.

Division and Applications.

Fractional Notation and Mixed Numerals

Least Common Multiples.

Addition and Multiplication.

Subtraction, Order, and Applications.

Mixed Numerals.

Addition and Subtraction Using Mixed Numerals; Applications.

Multiplication and Division Using Mixed Numerals: Applications.

Order of Operations; Estimation.

Decimal Notation

Decimal Notation, Order, and Rounding.

Addition and Subtraction with Decimal Notation.

Multiplication with Decimal Notation

Division with Decimal Notation.

Converting from Fractional to Decimal Notation.

Estimating.

Application and Problem Solving.

Ratio and Proportion

Introduction to Ratios.

Rates and Unit Prices.

Proportions.

Applicat6ions of Proportions.

Similar Triangles.

Percent Notation

Percent Notation and Fractional Notation.

Solving Percent Problems using Equations.

Solving Percent Problems using Proportions.

Applications of Percent.

Consumer Applications: Sales Tax, Commission, and Discount.

Consumer Applications: Interest.

Data Analysis, Graphs, and Statistics

Averages, Medians, and Modes.

Tables and Pictographs

Bar Graphs and Line Graphs

Circle Graphs

Data Analysis and Predictions

Geometry and Measures: Length and Area

Linear Measures: American Units.

Linear Measures: The Metric System.

Perimeter

Area

Areas of Parallelograms, Triangles, and Trapezoids

Circles

Square Roots and the Pythagorean Theorem

More Geometry and Measures

Volume and Capacity

Volume of Cylinders, Spheres, and Cones.

Weight, Mass, and Time.

Temperature

Converting Units of Area

Angles and Triangles

The Real-Number System

Addition of Real Numbers.

Subtraction of Real Numbers

Multiplication of Real Numbers

Division and Order of Operations

Algebra: Solving Equations and Problems

Introduction to Algebra

Solving Equations: The Addition Principle

Solving Equations: The Multiplication Principle

Using the Principles Together

Solving Application Problems

### BEGINNING ALGEBRA -

Real Numbers and Their Basic Properties

Real Numbers and their Graphs

Fractions

Exponents and Order of Operations

Adding and Subtracting Real Numbers

Multiplying and Dividing Real Numbers

Algebraic Expressions

Properties of Real Numbers

Equations and Inequalities

Introduction to Equations

Solving More Equations

Simplifying Expressions to Solve Equations

Literal Equations

Applications of Equations

More Applications of Equations

Solving Inequalities

Polynomials

Natural-Number Exponents

Zero and Negative Integral Exponents

Scientific Notation

Polynomials

Adding and Subtracting Polynomials

Multiplying Polynomials

Dividing Polynomials by Monomials

Dividing Polynomials by Polynomials

Factoring Polynomials

Factoring Out of the Greatest Common Factor

Factoring by Grouping

Factoring the Difference of Two Squares

Factoring Trinomials with Lead Coefficients of 1

Factoring General Trinomials

Factoring the Sum and Difference of Two Cubes

Summary of Factoring Techniques

Problem Solving

Rational Expressions

The Basic Properties of Fractions

Multiplying Fractions

Dividing Fractions

Adding and Subtracting Fractions with Like Denominators

Adding and Subtracting Fractions with Unlike Denominators

Complex Fractions

Solving Equations that Contain Fractions

Applications of Equations that contain Fractions

Ratio and Proportion

Graphing Linear Equations and Inequalities

Graphing Linear Equations

The Slope of a Line

Writing Equations of Lines

Graphs of Other Equations

Graphing Inequalities

Relations and Functions

Variation

Solving Systems of Equations and Inequalities

Solving Systems of Equations by Graphing

Solving Systems of Equations by Substitution

Solving Systems of Equations by Addition

Applications of Systems of Equations

Solving Systems of Linear Inequalities

Solving Systems of Three Equations in Three

Variables

Roots and Radical Expressions

Radicals

Simplifying Radical Expressions

Adding and Subtracting Radical Expressions

Multiplying and Dividing Radical Expressions

Solving Equations Containing Radicals

Rational Exponents

The Distance Formula

Quadratic Equations

Solving Equations of the Form x2=c

Completing the Square

The Quadratic Formula

Applications of Quadratic Equations

Complex Numbers

Graphing Quadratic Functions

### INTERMEDIATE ALGEBRA -

The Real Number System

Sets and the Real Number System

Equality and Properties of Real Numbers

Inequalities and Graphs of Real Numbers

Arithmetic of Real Numbers

Exponents and Polynomials

Exponents

Scientific Notation

Adding and Subtracting Polynomials

Multiplying Polynomials

Dividing Polynomials

Synthetic Division (Optional)

Equations and Inequalities

Linear Equations and Their Solutions

Applications

More Applications of Equations

Formulas and Literal Equations

Absolute Value Equations

Linear Inequalities

Inequalities with Absolute Values

Factoring Polynomials

The Greatest Common Factor

The Difference of Two Squares; the Sum and Difference of Two

Cubes

Factoring Trinomials

Summary of Factoring Techniques

Solving Equations by Factoring

Rational Expressions

Simplifying Rational Expressions

Multiplying and Dividing Rational Expressions

Adding and Subtracting Rational Expressions

Complex Fractions

Equations Containing Rational Expressions

Graphs, Equations of Lines, and Variation

The Rectangular Coordinate System

Slope of a Non-vertical Line

Equations of Lines

Graphs of Other Equations

Graphs of Linear Inequalities in Two Variables

Introduction to Functions

Proportion and Variation

Rational Exponents and Radicals

Rational Exponents

Radical Expressions

Adding and Subtracting Radical Expressions

Multiplying and Dividing Radical Expressions

Radical Equations

Applications of Radicals

Radicals with Different Orders (Optional)

Quadratic Equations

Completing the Square and the Quadratic Formula

Complex Numbers

More on Quadratic Equations

Graphs of Quadratic Equations

Quadratic and Other Nonlinear Inequalities

Systems of Equations and Inequalities

Solution by Graphing

Solution by Substitution and Addition

Solution of Three Equations in Three Variables

Determinants

Matrices

Systems of Inequalities

More Functions and Conic Sections

Polynomials and Other Functions

Algebra and Composition of Functions

Inverses of Functions

The Circle and the Parabola

The Ellipse and the Hyperbola

Solving Simaltaneous Second-Degree Equations

Exponential and Logarithmic Functions

Exponential Functions

Logarithmic Functions

Properties of Logarithms

Applications of Logarithms

Exponential and Logarithmic Equations

Miscellaneous Topics

The Binomial Theorem

The nth Term of a Binomial Expansion

Arithmetic Sequences

Geometric Sequences

Infinite Geometric Sequences

Permutations and Combinations

### COLLEGE ALGEBRA -

Prerequisites

Real Numbers

Exponents and Radicals

Polynomials and Special Products

Factoring

Fractional Expressions

Errors and the Algebra of Calculus

Graphical Representation of Data

Equations and Inequalities

Graphs and Graphing Utilities

Linear Equations

Modeling with Linear Equations

Quadratic Equations and Applications

Complex Numbers

Other Types of Equation

Linear Inequalities

Other Types of Inequalities

Functions and Their Graphs

Lines in the Plane and Slope

Functions

Analyzing Graphs of Functions

Translations and Combinations

Inverse Functions

Zeros of Polynomial Functions

Quadratic Functions

Polynomial Functions of Higher Degree

Polynomial and Synthetic Division

Real Zeros of Polynomial Functions

The Fundamental Theorem of Algebra

Mathematical Modeling

Rational Functions and Conics

Rational Functions and Asymptotes

Graphs and Rational Functions

Partial Fractions

Conics

Translations of Conics

Exponential and Logarithmic Functions

Exponential Functions and their Graphs

Logarithmic Functions and their Graphs

Properties of Logarithms

Exponential and Logarithmic Equations

Exponential and Logarithmic Models

Systems of Equations and Inequalities

Solving Systems of Equations

Two-Variable Linear Systems

Multivariable Linear Systems

Systems of Inequalities

Linear Programming

Matrices and Determinants

Matrices and Systems of Equations

Operations with Matrices

The Inverse of a Square Matrix

The Determinant of a Square Matrix

Applications of Matrices and Determinants

Sequences and Probability

Sequences and Summation Notation

Arithmetic Sequences

Geometric Sequences

Mathematical Induction

The Binomial Theorem

Counting Principles

Probability

### TRIGONOMETRY

Angles, Degrees & RadiansIntroduction to Trigonometric Functions

Trigonometric Functions of General Angles

Evaluating Trigonometric Functions

Graphing Trigonometric Functions

Trigonometric Identities

Inverse Trigonometric Functions

Trigonometric Equations

Right Triangle Applications

Law of Sines

Law of Cosines

Polar Coordinates

Trigonometric Form, Demoivre s Theorem & Nth Roots

of Complex Numbers

### PRECALCULUS

PrerequisitesReal Numbers

Exponents and Radicals

Polynomials and Factoring

Fractional Expressions

Solving Equations

Solving Inequalities

Errors and the Algebra of Calculus

Graphical Representation of Data

Functions and Their Graphs

Graphs & Graphing Utilities

Lines in the Plane and Slope

Functions

Analyzing Graphs of Functions

Translations and Combinations

Inverse Functions

Mathematical Modeling

Polynomial and Rational Functions

Quadratic Functions

Polynomial Functions of Higher Degree

Polynomial and Synthetic Division

Real Zeros of Polynomial Functions

Complex Numbers

The Fundamental Theorem of Algebra

Rational Functions

Partial Fractions

Exponential and Logarithmic Functions

Exponential Functions and their Graphs

Logarithmic Functions and their Graphs

Properties of Logarithms

Exponential and Logarithmic Functions

Exponential and Logarithmic Models

Trigonometry

Radian and Degree Measure

Trigonometric Functions: The Unit Circle

Right Triangle Trigonometry

Trigonometric Functions of Any Angle

Graphs of Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Inverse Trigonometric Functions

Applications and Models

Analytic Trigonometry

Using Fundamental Identities

Verifying Trigonometric Identities

Solving Trigonometric Equations

Sum and Difference Formulas

Multiple-Angle and Product-to-Sum Formulas

Additional Topics in Trigonometry

Law of Sines

Law of Cosines

Vectors in the Plane

Victors and Dot Products

DeMoivre s Theorem

Systems of Equations and Inequalities

Solving Systems of Equations

Two-Variable Linear Systems

Multivariable Linear Systems

Systems of Inequalities

Linear Programming

Matrices and Determinants

Matrices and Systems of Equations

Operations with Matrices

The Inverse of a Square Matrix

The Determinant of a Square Matrix

Application of Matrices and Determinants

Sequences and Probability

Sequences and Summation Notation

Arithmetic Sequences

Geometric Sequences

Mathematical Induction

The Binomial Theorem

Counting Principles

Probability

Topics in Analytic Geometry

Lines

Introduction to Conics: Parabolas

Ellipses

Hyperbolas

Rotation of Conics

Parametric Equations

Polar Coordinates

Graphs of Polar Equations

Polar Equations of Conics

### CALCULUS - Limits and their Properties

Definitions and Properties of Limits

Techniques for evaluating limits

Continuity and one-sided limits

Infinite limits

Differentiation

Derivatives and tangent lines

Velocity and other rates of change

Differentiation rules for sums, products, quotients, powers, and

Trigonometric functions

The chain rule

Differentiation

Related rules

Applications of Differentiation

Extremes on an interval

Rolle s Theorem and the Mean

Value Theorem

Increasing and decreasing functions and the first Derivative Test

Concavity and the Second Derivative Test

Limits at infinity

A summary of curve sketching

Optimization problems

Differentials

Integration

Antiderivatives and indefinite integration

Area

Riemann sums, and

The definite integral

Fundamental theorem of integral calculus

Integration by substitution

Transcendental Functions

The natural logarithm function

Inverse functions

Exponential functions

Applications

Inverse trigonometric functions

Differentiation, Integration, and

Completing the square

Hyperbolic functions

Applications of Integration

Area; Volumes; arc length

Surfaces of revolution

Work

Integration Techniques

Basic integration formulas

Integration by parts

Trigonometric integrals

Trigonometric substitution

More Integration TechniquesL Hopital s Rule

Partial fractions

Integrations by tables

Indeterminate forms and

L Hopital s rule

Improper integrals

Main