1. Fundamental Concepts of Algebra

Add and Subtract Rational Expressions

Rational Expressions

Rational Expressions:  Adding and Subtracting.  Ex 2

Simplifying Complex Fractions

Simplifying Complex Fractions - Ex 3

Adding and Subtracting Rational Expressions

Rational Expressions: Writing in Lowest Terms - Ex 2

Simplify each complex rational expression. (1/x-1/2)/(1/3-x/6)

Simplifying Complex Fractions - Ex 1

Rational Expressions:  Adding and Subtracting.  Ex 1

❖ Finding all the Zeros of a Polynomial - Example 3 ❖

Rational Expressions:  Multiplying and Dividing.  Ex 1

Simplify each rational expression. Also, list all numbers that must be excluded from the domain. [x^3+2x^2]/[x+2]

In Exercises 111–120, use the order of operations to simplify each expression. 10^2−100÷5^2⋅2−3

In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). 4+5(x-7)^3, for x =9

Simplify each complex rational expression. [3-1/(x+3)]/[3+1/(x+3)]

In Exercises 97–102, write each algebraic expression without parentheses. 1/3(3x)+[(4y)+(−4y)]

Finding the Domain of an Expression Involving Fractions - Example 3

How to Find Restrictions on Rational Expressions

Algebra - Complex Fractions

Multiply or divide as indicated. [(x^2+6x+9)(x+3)]/[(x^2-4)(x-2)]

In Exercises 111–120, use the order of operations to simplify each expression. 6(−4)−5(−3)/(9−10)

Subtracting rational expressions

In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). x^2-6x+3, for x=7

In Exercises 85–96, simplify each algebraic expression. 5(3y−2)−(7y+2)

In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). 6x-y, for x=3 and y=8

Rational Expressions:  Multiplying and Dividing.  Ex 3

In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). x^2+3x, for x=8

In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). x^2-3(x-y), for x=8 and y=2

In Exercises 85–96, simplify each algebraic expression. 18x^2+4−[6(x^2−2)+5]

Dividing rational expressions

In Exercises 33–68, add or subtract as indicated. 4/(x^2+6x+9) + 4/(x+3)

In Exercises 69–82, simplify each complex rational expression. (1/(x+h)^2 − 1/x^2)/h

Rational Expressions:  Multiplying and Dividing.  Ex 2

Multiply  Rational Expressions

Rational Expressions and Domain

Add or subtract as indicated. [(2x-7)/(x^2-9)]-[(x-10)/(x^2-9)]

In Exercises 85–96, simplify each algebraic expression. 5(3x+4)−4

Rewrite simple rational expressions using inspection

Add or subtract as indicated. 12/25x^2+11/15x^3

In Exercises 33–68, add or subtract as indicated. x/(x^2−2x−24) − x/(x^2−7x+6)

❖ Finding the Domain of a Function Algebraically (No graph!) ❖

In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). 7+5x, for x = 10

Finding the Domain of an Expression Involving Fractions - Example 2

Simplifying Complex Fractions - Ex 2

In Exercises 85–96, simplify each algebraic expression. 2(5x−1)+14x

Manipulating Rational Expressions: Simplification and Operations

In Exercises 69–82, simplify each complex rational expression. (x/3−1)/(x−3)

In Exercises 111–120, use the order of operations to simplify each expression. 8−3[−2(2−5)−4(8−6)]

Multiply rational expressions

Multiply or divide as indicated. [(x^2-5x-24)/(x^2-x-12)]/[(x^2-10x+16)/(x^2+x-6)]

Rational Expressions: Writing in Lowest Terms - Ex 1

In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). (2x+3y)/(x+1), for x=-2 and y=4

Rewrite polynomial expressions by factoring

In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). 5(x+2)/(2x-14), for x=10

Adding rational expressions

In Exercises 85–96, simplify each algebraic expression. 7−4[3−(4y−5)]

In Exercises 69–82, simplify each complex rational expression. (1/x + 1/y)/(x+y)

Finding all the Zeros of a Polynomial - Example 2

Finding the Domain of an Expression Involving Fractions - Example 1

Learn the toughest concepts covered in Algebra with step-by-step video tutorials and practice problems by world-class tutors

College Algebra

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2. Equations and Inequalities

3. Functions and Graphs

4. Polynomial and Rational Functions

5. Exponential and Logarithmic Functions

6. Systems of Equations and Inequalities

7. Matrices and Determinants

8. Conic Sections

9. Sequences, Induction, and Probability

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Understand the Vocabulary of Polynomials

Add and Subtract Polynomials

Multiply Polynomials

Use FOIL in Polynomial Multiplication

Use Special Products in Polynomial Multiplication

Perform Operations with Polynomials in Several Variables

Polynomials

Use the Product Rule

Use the Quotient Rule

Use the Zero-Exponent Rule

The Negative-Exponent Rule

The Power Rule

Find the Power of a Product

Find the Power of a Quotient

Simplify Exponential Expressions

Use Scientific Notation

Exponents and Scientific Notation

Evaluate Algebraic Expressions 

Usage Mathematical Models

Union & Intersection Of Two Sets

Recognize Real Numbers

Use Inequality Symbols

Evaluate Absolute Value

Use Absolute Value to Express Distance

Identify Properties of the Real Numbers

Simplify Algebraic Expressions

Expressions, Models, Real Numbers

Factor out the Greatest Common Factor of a Polynomial

Factor by Grouping

Factor Trinomials

Factor the Difference of Squares

Factor Perfect Square Trinomials

Factor the Sum or Difference of Two Cubes

Use a General Strategy for Factoring Polynomials

Factor Algebraic Expressions Containing Fractional and Negative Exponents

Factoring Polynomials

Specify Numbers that Must be Excluded From the Domain of a Rational Expression

Simplify Rational Expressions

Multiply Rational Expressions

Divide Rational Expressions

Simplify Complex Rational Expressions

Evaluate Square Roots

Simplify Expressions of the Form &radic; <i>a</i><sup>2</sup>

Use the Product Rule to Simplify Square Roots

Use the Quotient Rule to Simplify Square Roots

Add and Subtract Square Roots

Rationalize Denominators

Evaluate and Perform Operations with Higher Roots

Understand and Use Rational Exponents

Radicals and Rational Exponents

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